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(c:/swp55/TCITeX/tex/latex/amsfonts/umsb.fd File: umsb.fd 2002/01/19 v2.2g AMS font definitions ) [1 {c:/swp55/TCITeX/fonts/map/pdftex/pdftex.map}] [2 ] LaTeX Font Info: Font shape `T1/ptm/bx/n' in size <20.74> not available (Font) Font shape `T1/ptm/b/n' tried instead on input line 98. (./swp0000.toc LaTeX Font Info: Font shape `T1/ptm/bx/n' in size <12> not available (Font) Font shape `T1/ptm/b/n' tried instead on input line 3. [3] [4] Underfull \vbox (badness 1152) has occurred while \output is active [] [5] [6]) \tf@toc=\write6 \openout6 = `swp0000.toc'. (./intro.tex Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\noindent' on input line 10. [1] [2] [3] [4] [5] LaTeX Font Warning: Command \small invalid in math mode on input line 478. [6]) (./PlanComplexe.tex [7] [8 ] 1. [9] [10] [11] [12] [13] [14] LaTeX Font Info: Font shape `T1/ptm/bx/it' in size <12> not available (Font) Font shape `T1/ptm/b/it' tried instead on input line 670. File: C:/Users/VJM/Documents/Dropbox/3M266/Livre/graphics/cercles__1.jpg Graphi c file (type jpg) Underfull \vbox (badness 7851) has occurred while \output is active [] [15]) (./FctionsHolomorphes.tex [16 ] 2. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 12. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 12. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 12. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 12. [17 ] Overfull \hbox (43.73305pt too wide) in paragraph at lines 208--216 []\T1/ptm/m/n/12 Une ap-pli-ca-tion $\U/msb/m/n/12 C$\T1/ptm/m/n/12 -lin^^e9air e ^^e9tant en par-ti-cu-lier $\U/msb/m/n/12 R$\T1/ptm/m/n/12 -lin^^e9aire, la $ \U/msb/m/n/12 C$\T1/ptm/m/n/12 -diff^^e9rentiabilit^^e9 en-tra^^eene la $\U/msb /m/n/12 R$\T1/ptm/m/n/12 -diff^^e9rentiabilit^^e9, [] [18] [19] Overfull \hbox (8.51123pt too wide) in paragraph at lines 410--413 []\T1/ptm/m/it/12 Le rayon de conver-gence $\OML/cmm/m/it/12 R$ \T1/ptm/m/it/12 d'une s^^e9-rie en-ti^^e8re $[]$ [] [20] Underfull \hbox (badness 10000) in paragraph at lines 501--503 [] [21] [22] [23] [24] Overfull \hbox (5.1279pt too wide) in paragraph at lines 881--885 []\T1/ptm/m/it/12 Soient $\OML/cmm/m/it/12 U$ \T1/ptm/m/it/12 un ou-vert de $\U /msb/m/n/12 C$ \T1/ptm/m/it/12 et $\OML/cmm/m/it/12 f \OT1/cmr/m/n/12 : \OML/cm m/m/it/12 U \OMS/cmsy/m/n/12 ! \U/msb/m/n/12 C$ \T1/ptm/m/it/12 une ap-pli-ca-t ion $\U/msb/m/n/12 R$\T1/ptm/m/it/12 -diff^^e9rentiable. [] [25] Overfull \hbox (20.19771pt too wide) in paragraph at lines 1060--1063 []\T1/ptm/m/it/12 Les fonc-tions $[]$ et $[]$ sont ho-lo-morphes et v^^e9-ri-fi ent $[][] \OT1/cmr/m/n/12 = \OMS/cmsy/m/n/12 ^^@ []$\T1/ptm/m/it/12 , $[][] \OT 1/cmr/m/n/12 = []$\T1/ptm/m/it/12 , $[][] \OT1/cmr/m/n/12 + [][] = [] [26] [27] Overfull \hbox (13.3142pt too wide) in paragraph at lines 1193--1203 []$\U/msa/m/n/12 N$ \T1/ptm/m/n/12 Si $\OML/cmm/m/it/12 z \OMS/cmsy/m/n/12 2 \U /msb/m/n/12 C$\T1/ptm/m/n/12 , $[] [] \OT1/cmr/m/n/12 = [] [] = [] [] = [] \OML /cmm/m/it/12 z$\T1/ptm/m/n/12 . Par cons^^e9-quent, $[][] [] \OT1/cmr/m/n/12 = [] Overfull \hbox (16.1871pt too wide) in paragraph at lines 1230--1234 \T1/ptm/b/n/12 Remarque. \T1/ptm/m/n/12 Bien en-tendu $[]$ et $[]$ sont d^^e9-r i-vables sur $[]$ et lorsque $\OML/cmm/m/it/12 x \OMS/cmsy/m/n/12 2 []$\T1/ptm/ m/n/12 , $[] [][] [] \OT1/cmr/m/n/12 = [] [28] [29] [30] [31] [32] [33] [34] [35] Overfull \hbox (3.6643pt too wide) in paragraph at lines 2024--2027 []\T1/ptm/m/it/12 En pre-nant la d^^e9-ter-mi-na-tion prin-ci-pale de la puis-s ance $\OML/cmm/m/it/12 j \OT1/cmr/m/n/12 = \OML/cmm/m/it/12 e[]$\T1/ptm/m/it/12 , cal-cu-ler $[][]$ [] ) (./TheorieCauchy.tex [36] 3. Overfull \hbox (12.76729pt too wide) in paragraph at lines 43--48 []\T1/ptm/m/it/12 Soient $\OML/cmm/m/it/12 U$ \T1/ptm/m/it/12 un ou-vert de $\U /msb/m/n/12 C$\T1/ptm/m/it/12 , $\OML/cmm/m/it/12 f \OMS/cmsy/m/n/12 2 \OML/cmm /m/it/12 C[] []$ \T1/ptm/m/it/12 et $[] \OMS/cmsy/m/n/12 2 C\OML/cmm/m/it/12 h[ ] []$\T1/ptm/m/it/12 . [] Overfull \hbox (10.76848pt too wide) in paragraph at lines 51--55 \T1/ptm/m/it/12 En par-ti-cu-lier, si $[]$ est un la-cet \T1/ptm/b/it/12 et \T1 /ptm/m/it/12 si $\OML/cmm/m/it/12 f$ \T1/ptm/m/it/12 ad-met une pri-mi-tive ho- lo-morphe au voi-si-nage de $[]$, $[][] \OML/cmm/m/it/12 f [] dz \OT1/cmr/m/n/1 2 = [] [37 ] [38] File: C:/Users/VJM/Documents/Dropbox/3M266/Livre/graphics/TRI1__1.jpg Graphic f ile (type jpg) [39 ] File: C:/Users/VJM/Documents/Dropbox/3M266/Livre/graphics/TRI2__2.jpg Graphic f ile (type jpg) File: C:/Users/VJM/Documents/Dropbox/3M266/Livre/graphics/TRI3__3.jpg Graphic f ile (type jpg) File: C:/Users/VJM/Documents/Dropbox/3M266/Livre/graphics/TRI4__4.jpg Graphic f ile (type jpg) [40 ] [41] [42] [43] [44] [45] [46] Overfull \hbox (0.75273pt too wide) in paragraph at lines 1049--1055 []\T1/ptm/m/it/12 Soit $[] \OMS/cmsy/m/n/12 2 L\OML/cmm/m/it/12 a[] []$\T1/ptm/ m/it/12 . Alors $[] []$ prend ses va-leurs dans $\U/msb/m/n/12 Z$\T1/ptm/m/it/1 2 , est constante [] [47] [48] [49] [50] [51] File: C:/Users/VJM/Documents/Dropbox/3M266/Livre/graphics/HomotopieInit__5.jpg Graphic file (type jpg) [52 ] File: C:/Users/VJM/Documents/Dropbox/3M266/Livre/graphics/HomotopieInduc__6.jpg Graphic file (type jpg) [53 ] Overfull \hbox (23.41208pt too wide) in paragraph at lines 1852--1855 []\T1/ptm/m/it/12 Pour $\OML/cmm/m/it/12 n \OMS/cmsy/m/n/12 2 \U/msb/m/n/12 N$\ T1/ptm/m/it/12 , cal-cu-ler $[] [][] [][] []$. En d^^e9-duire la va-leur des in -t^^e9-grales $[][] [][] [] \OML/cmm/m/it/12 dt$ [] [54] Overfull \hbox (23.46756pt too wide) in paragraph at lines 1935--1939 []\T1/ptm/m/it/12 Soient $\OML/cmm/m/it/12 U$ \T1/ptm/m/it/12 un ou-vert de $\U /msb/m/n/12 C$ \T1/ptm/m/it/12 conte-nant $[]$, $\OML/cmm/m/it/12 f \OMS/cmsy/m /n/12 2 O []$ \T1/ptm/m/it/12 et $\OML/cmm/m/it/12 a \OMS/cmsy/m/n/12 2 \OML/cm m/m/it/12 U\OMS/cmsy/m/n/12 n\U/msb/m/n/12 T$\T1/ptm/m/it/12 . Prou-ver que $[] [][] []\OML/cmm/m/it/12 dz \OT1/cmr/m/n/12 = [] [55] [56]) (./PropFondHolo.tex [57] [58 ] 4. [59] [60] Overfull \hbox (12.55228pt too wide) in paragraph at lines 266--279 \T1/ptm/m/n/12 lorsque $\OML/cmm/m/it/12 z \OMS/cmsy/m/n/12 2 \OML/cmm/m/it/12 D []$ \T1/ptm/m/n/12 et $[] \OT1/cmr/m/n/12 = \OML/cmm/m/it/12 d[] []$\T1/ptm/m /n/12 . On ob-tient alors que si $\OT1/cmr/m/n/12 0 \OML/cmm/m/it/12 < [] << \O T1/cmr/m/n/12 1$\T1/ptm/m/n/12 , $\OML/cmm/m/it/12 f [] \OT1/cmr/m/n/12 = [] \O ML/cmm/m/it/12 c[] [][]$\T1/ptm/m/n/12 . [] Overfull \hbox (17.93045pt too wide) in paragraph at lines 293--297 []\T1/ptm/m/it/12 Soit $\OML/cmm/m/it/12 f$ \T1/ptm/m/it/12 une fonc-tion conti -nue sur un disque ou-vert $\OT1/cmr/m/n/12 ^^A = \OML/cmm/m/it/12 D []$ \T1/pt m/m/it/12 telle que $[][] \OML/cmm/m/it/12 f [] dz \OT1/cmr/m/n/12 = [] [61] [62] [63] [64] Overfull \hbox (11.75182pt too wide) in paragraph at lines 603--616 \OML/cmm/m/it/12 D []$ \T1/ptm/m/n/12 re-la-ti-ve-ment com-pact dans $\OML/cmm/ m/it/12 U$\T1/ptm/m/n/12 . On pose $\OT1/cmr/m/n/12 ^^A[] = ^^A []$ \T1/ptm/m/n /12 o^^f9 $\OML/cmm/m/it/12 R[] \OT1/cmr/m/n/12 = \OML/cmm/m/it/12 R \OT1/cmr/m /n/12 + []$ \T1/ptm/m/n/12 avec $[] \OT1/cmr/m/n/12 = []\OML/cmm/m/it/12 dist [ ]$ [] [65] [66] [67] [68] [69] [70] [71] [72]) (./Residus.tex [73] [74 ] 5. [75] Underfull \vbox (badness 1163) has occurred while \output is active [] [76] [77] [78] Overfull \hbox (5.02423pt too wide) in paragraph at lines 371--375 []\T1/ptm/m/it/12 Soit $\OML/cmm/m/it/12 f$ \T1/ptm/m/it/12 une fonc-tion ho-lo -morphe sur $\OT1/cmr/m/n/12 ^^A[] = [] [79] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\new@ifnextchar' on input line 537. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\smallskipamount' on input line 537. [80] [81] File: C:/Users/VJM/Documents/Dropbox/3M266/Livre/graphics/Residu__1.jpg Graphic file (type jpg) [82 ] [83] [84] [85] [86] [87] [88] [89] [90] [91] [92]) (./FonctionsHarmoniques.tex [93] [94 ] 6. Overfull \hbox (30.90294pt too wide) in paragraph at lines 101--112 []\T1/ptm/b/n/12 Preuve. \T1/ptm/m/n/12 Soit $\OT1/cmr/m/n/12 $ \T1/ptm/m/n/12 un do-maine sim-ple-ment connexe. Il s'agit de prou-ver que $\ OMS/cmsy/m/n/12 H [] ^^Z []$\T1/ptm/m/n/12 , [] [95] [96] Overfull \hbox (4.87457pt too wide) in paragraph at lines 214--230 []\T1/ptm/m/n/12 1) Sup-po-sons que $\OML/cmm/m/it/12 u \OMS/cmsy/m/n/12 2 H [] $ \T1/ptm/m/n/12 pos-s^^e8de un maxi-mum lo-cal en $\OML/cmm/m/it/12 a \OMS/cms y/m/n/12 2 \OML/cmm/m/it/12 D$\T1/ptm/m/n/12 . D'apr^^e8s le (1) du lemme []4.2 3[], [] [97] [98] [99] [100] [101pdfTeX warning (ext4): destination with the same ident ifier (name{equation.6.4.9}) has been already used, duplicate ignored \AtBegShi@Output ...ipout \box \AtBeginShipoutBox \fi \fi l.690 \end{equation*} %] [102] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 798. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `superscript' on input line 798. 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[103] [104] [105] Overfull \hbox (20.38094pt too wide) in paragraph at lines 1087--1091 []\T1/ptm/m/it/12 D^^e9terminer les ap-pli-ca-tions $\OML/cmm/m/it/12 f$ \T1/pt m/m/it/12 de $\U/msb/m/n/12 R[]$ \T1/ptm/m/it/12 dans $\U/msb/m/n/12 R$ \T1/ptm /m/it/12 de classe $\OML/cmm/m/it/12 C[]$ \T1/ptm/m/it/12 telles que $\OML/cmm/ m/it/12 u[] \OT1/cmr/m/n/12 : \OML/cmm/m/it/12 z \OMS/cmsy/m/n/12 7! \OML/cmm/m /it/12 f []$ [] Overfull \hbox (10.80531pt too wide) in paragraph at lines 1169--1173 []\T1/ptm/b/it/12 3. \T1/ptm/m/it/12 D^^e9-ter-mi-ner l'en-semble $\OMS/cmsy/m/ n/12 C$ \T1/ptm/m/it/12 des fonc-tions $\OML/cmm/m/it/12 h \OMS/cmsy/m/n/12 2 \ OML/cmm/m/it/12 C[] []$ \T1/ptm/m/it/12 ho-lo-morphes sur $\OML/cmm/m/it/12 D$ \T1/ptm/m/it/12 telles que $[] [] \OT1/cmr/m/n/12 = [] [106]) (./ProprietesAvancees.tex [107] [108 ] 7. [109] [110] [111] Overfull \hbox (1.71303pt too wide) in paragraph at lines 340--348 []\T1/ptm/m/n/12 R^^e9ciproquement, sup-po-sons $[]$ v^^e9-ri-fi^^e9e. Il exist e donc $\OML/cmm/m/it/12 N[] \OMS/cmsy/m/n/12 2 \U/msb/m/n/12 N$ \T1/ptm/m/n/12 tel que $[][] \OT1/cmr/m/n/12 = ([] \OML/cmm/m/it/12 a[]\OT1/cmr/m/n/12 )[]$ [] [112] [113] Overfull \hbox (47.26768pt too wide) in paragraph at lines 555--564 \T1/ptm/m/n/12 nue et $\OML/cmm/m/it/12 K$ \T1/ptm/m/n/12 com-pact, la conver-g ence uni-forme de $[]$ sur $\OML/cmm/m/it/12 K$ \T1/ptm/m/n/12 vers $\OML/cmm/m /it/12 F[]$ \T1/ptm/m/n/12 en-tra^^eene celle de $[][]$, [] [114] [115] [116] [117] [118] [119] Overfull \hbox (7.39572pt too wide) in paragraph at lines 1146--1150 []\T1/ptm/m/it/12 Soient $\OML/cmm/m/it/12 D$ \T1/ptm/m/it/12 un do- [] [120] [121] [122] [123] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 1479. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\left' on input line 1479. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\right' on input line 1479. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 1479. Overfull \hbox (10.62039pt too wide) in paragraph at lines 1535--1542 []\T1/ptm/b/n/12 Preuve. \T1/ptm/m/n/12 Soient $\OML/cmm/m/it/12 f; g; h \OMS/c msy/m/n/12 2 \OML/cmm/m/it/12 C[] []$\T1/ptm/m/n/12 . La s^^e9-rie ^^e9crite da ns ([]7.19[]) est conver-gente puisque $\OT1/cmr/m/n/12 0 \U/msa/m/n/12 6 []\OM L/cmm/m/it/12 d[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 f; g\OT1/cmr/m/n/12 ) \U/msa /m/n/12 6 [] [124] [125] [126] Overfull \hbox (1.03928pt too wide) in paragraph at lines 1850--1853 []\T1/ptm/m/it/12 Soient $\OML/cmm/m/it/12 D$ \T1/ptm/m/it/12 un do-maine de $\ U/msb/m/n/12 C$ \T1/ptm/m/it/12 et $[]$ une suite bor-n^^e9e de $\OMS/cmsy/m/n/ 12 O []$\T1/ptm/m/it/12 . [] [127] [128] Overfull \hbox (7.37788pt too wide) in alignment at lines 2007--2018 [][][] [] [] [129] [130] Overfull \hbox (2.89906pt too wide) in paragraph at lines 2233--2236 []\T1/ptm/m/it/12 Soit $\OMS/cmsy/m/n/12 F$ \T1/ptm/m/it/12 un sous-ensemble de $\OMS/cmsy/m/n/12 O []$\T1/ptm/m/it/12 . Les [] [131] [132] [133] [134] Overfull \hbox (2.00063pt too wide) in paragraph at lines 2642--2645 []\T1/ptm/m/it/12 Soit $\OML/cmm/m/it/12 f \OMS/cmsy/m/n/12 2 O []$\T1/ptm/m/it /12 . Si $\OML/cmm/m/it/12 f$ \T1/ptm/m/it/12 n'est pas constante, $\U/msb/m/n/ 12 C\OMS/cmsy/m/n/12 n\OML/cmm/m/it/12 f []$ [] [135] [136] [137] [138] [139] [140] LaTeX Font Warning: Command \sl invalid in math mode on input line 3375. [141] Overfull \hbox (2.80083pt too wide) in paragraph at lines 3413--3417 []\T1/ptm/b/it/12 d) \T1/ptm/m/it/12 Prou-ver que $[] \U/msa/m/n/12 6 [][]$ \T1 /ptm/m/it/12 sur $\U/msb/m/n/12 D$ \T1/ptm/m/it/12 et ^^e9tu-diant $[]$, conclu re ^^e0 la conver-gence de $[]$. [] [142] [143]) (./RepresentationConforme.tex [144] [145] [146 ] 8. [147] [148] Overfull \hbox (6.08899pt too wide) in paragraph at lines 256--259 []\T1/ptm/m/it/12 Soit $\OT1/cmr/m/n/12 $ \T1/ptm/m/it/12 un do-maine sim- [] [149] [150] [151] [152] [153] [154] File: C:/Users/VJM/Documents/Dropbox/3M266/Livre/graphics/Kobe__1.jpg Graphic f ile (type jpg) Overfull \hbox (14.02501pt too wide) in paragraph at lines 949--959 \T1/ptm/m/n/12 lemme []3.20[], on sait que si $\OMS/cmsy/m/n/12 A$ \T1/ptm/m/n/ 12 est une d^^e9-ter-mi-na-tion conti-nue de l'ar-gu-ment le long de $\OT1/cmr/ m/n/12 ^^@[]$\T1/ptm/m/n/12 , $\OT1/cmr/m/n/12 2[] [] [] = [] [155 ] [156] Overfull \hbox (2.07083pt too wide) in paragraph at lines 1130--1138 []\T1/ptm/m/n/12 Soit $\OML/cmm/m/it/12 r \OMS/cmsy/m/n/12 2 []$\T1/ptm/m/n/12 . Lorsque $\OML/cmm/m/it/12 j \OMS/cmsy/m/n/12 2 []$\T1/ptm/m/n/12 , $\OT1/cmr/ m/n/12 ^^@[] []$ \T1/ptm/m/n/12 est un connexe qui ren-contre $[]$ et $\U/msb/m /n/12 C\OMS/cmsy/m/n/12 n[]$ [] [157] [158] [159]) (./Runge.tex [160] 9. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 8. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\@@overline' on input line 8. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\partial' on input line 8. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 8. Overfull \hbox (4.74922pt too wide) in paragraph at lines 21--23 []\T1/ptm/m/n/12 Afin d'al-l^^e9-ger la lec-ture des preuves, on ^^e9crit dans ce cha-pitre \T1/ptm/m/it/12 com-po-sante \T1/ptm/m/n/12 pour \T1/ptm/m/it/12 c om-po-sante connexe\T1/ptm/m/n/12 . [] [161 ] Overfull \vbox (0.7941pt too high) has occurred while \output is active [] [162] Overfull \vbox (0.7941pt too high) has occurred while \output is active [] [163] Overfull \vbox (0.7941pt too high) has occurred while \output is active [] [164] Overfull \vbox (0.7941pt too high) has occurred while \output is active [] [165] Overfull \vbox (0.7941pt too high) has occurred while \output is active [] [166] Overfull \vbox (0.7941pt too high) has occurred while \output is active [] [167] Overfull \vbox (0.7941pt too high) has occurred while \output is active [] [168] Overfull \vbox (0.7941pt too high) has occurred while \output is active [] [169] Overfull \vbox (0.7941pt too high) has occurred while \output is active [] [170] Overfull \hbox (0.86023pt too wide) in paragraph at lines 1142--1145 []\T1/ptm/m/n/12 Pour r^^e9-pondre ^^e0 ces ques-tions, on peut pen-ser ^^e0 ut i-li-ser un th^^e9o-r^^e8me clas-sique de Stone-Weierstrass[] : [] Overfull \vbox (0.7941pt too high) has occurred while \output is active [] [171] Overfull \vbox (0.7941pt too high) has occurred while \output is active [] [172] Overfull \vbox (0.7941pt too high) has occurred while \output is active [] [173] Overfull \vbox (0.7941pt too high) has occurred while \output is active [] [174] Overfull \vbox (0.7941pt too high) has occurred while \output is active [] [175] Overfull \vbox (0.7941pt too high) has occurred while \output is active [] [176] Overfull \vbox (0.7941pt too high) has occurred while \output is active [] [177] Overfull \vbox (0.7941pt too high) has occurred while \output is active [] [178] Overfull \vbox (0.7941pt too high) has occurred while \output is active [] [179]) (./ML-W.tex Overfull \vbox (0.7941pt too high) has occurred while \output is active [] [180] 10. [181 ] Overfull \hbox (4.1554pt too wide) in paragraph at lines 111--118 \T1/ptm/m/n/12 o^^f9 $\OML/cmm/m/it/12 T[]$ \T1/ptm/m/n/12 est une fonc-tion po -ly-n^^f4me choi-sie de la ma-ni^^e8re sui-vante : $\OML/cmm/m/it/12 L[] \OT1/c mr/m/n/12 : \OML/cmm/m/it/12 D [] \OMS/cmsy/m/n/12 3 \OML/cmm/m/it/12 z \OMS/cm sy/m/n/12 7! [] []$ [] [182] [183] [184] [185] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 591. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\left' on input line 591. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\right' on input line 591. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 591. 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Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 1064. [191] [192] [193] [194] [195] [196] LaTeX Font Info: Try loading font information for U+euf on input line 1763. (c:/swp55/TCITeX/tex/latex/amsfonts/ueuf.fd File: ueuf.fd 2002/01/19 v2.2g AMS font definitions ) Overfull \hbox (3.63702pt too wide) in paragraph at lines 1815--1822 []\T1/ptm/m/n/12 Puisque $\OT1/cmr/m/n/12 ^^E[]$ \T1/ptm/m/n/12 est le pro-duit des fonc-tions $\OML/cmm/m/it/12 z \OMS/cmsy/m/n/12 7! \OML/cmm/m/it/12 f []$\ T1/ptm/m/n/12 , on en d^^e9-duit que $[] \U/msa/m/n/12 6 \OML/cmm/m/it/12 e[]$\ T1/ptm/m/n/12 avec [] [197] [198] [199] [200] [201]) (./FonctionsClassiques.tex [202] 11. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 33. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\Gamma' on input line 33. 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Overfull \hbox (4.43361pt too wide) in paragraph at lines 258--267 []\T1/ptm/m/n/12 En d^^e9-ve-lop-pant $[]$ en s^^e9-rie en-ti^^e8re, on ob-tien t que pour tout $[] \OMS/cmsy/m/n/12 2 \U/msb/m/n/12 C \OMS/cmsy/m/n/12 ^^B \U/ msb/m/n/12 R[]$\T1/ptm/m/n/12 , $[] [] \OT1/cmr/m/n/12 = [] [][] []$ [] [205] [206] [207] [208] [209pdfTeX warning (ext4): destination with the same id entifier (name{equation.11.1.15}) has been already used, duplicate ignored \AtBegShi@Output ...ipout \box \AtBeginShipoutBox \fi \fi l.647 ] [210] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 799. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\Gamma' on input line 799. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 799. [211] Overfull \hbox (34.36163pt too wide) in paragraph at lines 846--852 \T1/ptm/m/n/12 avec $\OML/cmm/m/it/12 A[] [] \OT1/cmr/m/n/12 = [] \OML/cmm/m/it /12 a[]X[] \OT1/cmr/m/n/12 = []![] []$\T1/ptm/m/n/12 . Pour ce qu'il suit, on p ose$\OMS/cmsy/m/n/12 M [] \OT1/cmr/m/n/12 = [] \OMS/cmsy/m/n/12 n []$\T1/ptm/m/ n/12 . [] [212] [213] [214] Overfull \hbox (8.26201pt too wide) in paragraph at lines 1174--1182 \T1/ptm/m/n/12 voir $\OML/cmm/m/it/12 CY[]$\T1/ptm/m/n/12 , n'est donc pas di-v i-sible par $\OML/cmm/m/it/12 X \OMS/cmsy/m/n/12 ^^@ \OT1/cmr/m/n/12 1$\T1/ptm/ m/n/12 . $\OML/cmm/m/it/12 G []$ \T1/ptm/m/n/12 ne l'est pas non plus et $\OML/ cmm/m/it/12 G []$ [] [215] [216] [217] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 1429. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 1429. [218] [219] File: C:/Users/VJM/Documents/Dropbox/3M266/Livre/graphics/zeta1__1.jpg Graphic file (type jpg) Overfull \hbox (25.37555pt too wide) in paragraph at lines 1658--1667 \T1/ptm/m/n/12 po-sant $\OML/cmm/m/it/12 L[] [] \OT1/cmr/m/n/12 = [] [] + \OML/ cmm/m/it/12 i[]$ \T1/ptm/m/n/12 quand $\OML/cmm/m/it/12 t \OMS/cmsy/m/n/12 2 \U /msb/m/n/12 R[]$ \T1/ptm/m/n/12 et no-tons $\OML/cmm/m/it/12 L[]$ \T1/ptm/m/n/1 2 le pro-lon-ge-ment par conti-nuit^^e9 de $[] []$ [] [220 ] [221] File: C:/Users/VJM/Documents/Dropbox/3M266/Livre/graphics/Zeta2__2.jpg Graphic file (type jpg) [222 ] [223] [224] [225] [226] [227] Overfull \hbox (6.05743pt too wide) in paragraph at lines 2370--2375 \T1/ptm/m/n/12 Notons $\OML/cmm/m/it/12 C[]$ \T1/ptm/m/n/12 (resp. $\OML/cmm/m/ it/12 C[]$\T1/ptm/m/n/12 ) le che-min ob-tenu comme res-tric-tion de $\OML/cmm/ m/it/12 @K[]$ \T1/ptm/m/n/12 et dont le sup-port est $[] \OMS/cmsy/m/n/12 \ [] [228] [229] [230] [231] File: C:/Users/VJM/Documents/Dropbox/3M266/Livre/graphics/Qmodulaire__3.jpg Gra phic file (type jpg) [232 ] [233] [234] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 3097. 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Overfull \hbox (2.38199pt too wide) in paragraph at lines 3115--3119 []\T1/ptm/m/it/12 (b) $[] []$ est in-jec-tive, $[]$ est lo-ca-le-ment in-jec-ti ve et pour tout $\OML/cmm/m/it/12 z \OMS/cmsy/m/n/12 2 \U/msb/m/n/12 H$\T1/ptm/ m/it/12 , $[][] [] \OT1/cmr/m/n/12 = []$\T1/ptm/m/it/12 , [] [235] [236] [237] [238] [239] Overfull \hbox (5.12787pt too wide) in paragraph at lines 3645--3652 $\OML/cmm/m/it/12 a \OMS/cmsy/m/n/12 2 \U/msb/m/n/12 C$\T1/ptm/m/n/12 , sont ap -pe-l^^e9s pa-ral-l^^e9-lo-grammes de p^^e9-riodes[]. $\U/msb/m/n/12 C$ \T1/ptm /m/n/12 ^^e9tant la r^^e9union dis-jointe des $\OT1/cmr/m/n/12 ^^E[] []$ [] [240] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 3784. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\wp' on input line 3784. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 3784. [241] [242] [243] Overfull \hbox (7.51057pt too wide) in paragraph at lines 4043--4055 []\T1/ptm/m/n/12 Soit $\OT1/cmr/m/n/12 ^^E$ \T1/ptm/m/n/12 un pa-ral-l^^e9-lo-g ramme de p^^e9-riodes et $\OML/cmm/m/it/12 a \OMS/cmsy/m/n/12 2 \OT1/cmr/m/n/12 ^^E$ \T1/ptm/m/n/12 un z^^e9ro de $\OML/cmm/m/it/12 f$ \T1/ptm/m/n/12 de mul-t i-pli-cit^^e9 $\OML/cmm/m/it/12 m$\T1/ptm/m/n/12 . Se-lon le lemme []11.56[] [] Overfull \hbox (12.63051pt too wide) in paragraph at lines 4103--4107 \T1/ptm/m/n/12 est une fonc-tion el-lip-tique sans z^^e9ro. Elle est donc const ante, gr^^e2ce au co-rol-laire []11.53[] et au lemme []11.51[]. [] [244] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 4197. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\wp' on input line 4197. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 4197. [245] Overfull \hbox (15.93164pt too wide) in paragraph at lines 4262--4272 []$\U/msa/m/n/12 N$ \T1/ptm/m/n/12 Soit $\OML/cmm/m/it/12 z \OMS/cmsy/m/n/12 2 \U/msb/m/n/12 H$\T1/ptm/m/n/12 . Etant donn^^e9 que $\OML/cmm/m/it/12 }[]$ \T1/ ptm/m/n/12 est en par-ti-cu-lier p^^e9-rio-dique de p^^e9-riode $\OT1/cmr/m/n/1 2 1$\T1/ptm/m/n/12 , $\OML/cmm/m/it/12 w \OMS/cmsy/m/n/12 7! \OML/cmm/m/it/12 } [] []$ [] [246] [247pdfTeX warning (ext4): destination with the same identifier (name{equ ation.11.4.59}) has been already used, duplicate ignored \AtBegShi@Output ...ipout \box \AtBeginShipoutBox \fi \fi l.4413 \end{eqnarray*} %pdfTeX warning (ext4): destination with the same identif ier (name{equation.11.4.60}) has been already used, duplicate ignored \AtBegShi@Output ...ipout \box \AtBeginShipoutBox \fi \fi l.4413 \end{eqnarray*} %] [248] [249] Overfull \hbox (14.8043pt too wide) in paragraph at lines 4635--4655 \T1/ptm/m/n/12 Comme $[] [] \OMS/cmsy/m/n/12 2 \U/msb/m/n/12 R[]$\T1/ptm/m/n/12 , cette fonc-tion est conti-nue sur $[] \OMS/cmsy/m/n/12 n []$\T1/ptm/m/n/12 . On sait par ailleurs que $[] [] \OMS/cmsy/m/n/12 2 [] Overfull \hbox (15.32278pt too wide) in paragraph at lines 4635--4655 [] [] [] \OMS/cmsy/m/n/12 2 []$\T1/ptm/m/n/12 . Par contre, la for-mule ci-dess us livre que $[][] [] [] [] [] \OMS/cmsy/m/n/12 L [] \OT1/cmr/m/n/12 = [] Overfull \hbox (27.45218pt too wide) in paragraph at lines 4661--4672 \T1/ptm/m/n/12 pliquent que $[]$ est contenu dans $[]$ si $\OML/cmm/m/it/12 A$ \T1/ptm/m/n/12 est as-sez grand. Pour de tels $\OML/cmm/m/it/12 A$\T1/ptm/m/n/1 2 , $[] [] \OT1/cmr/m/n/12 = [] [250] Overfull \hbox (3.32196pt too wide) in paragraph at lines 4729--4735 []\T1/ptm/m/it/12 On consi-d^^e8re le che-min (non born^^e9) $[] \OT1/cmr/m/n/1 2 : \U/msb/m/n/12 R \OMS/cmsy/m/n/12 ! [] Overfull \hbox (20.77594pt too wide) in paragraph at lines 4803--4806 []\T1/ptm/b/it/12 1. \T1/ptm/m/it/12 Prou-ver en uti-li-sant une for-mule in-t^ ^e9-grale que la fonc-tion $\OT1/cmr/m/n/12 ^^@$ \T1/ptm/m/it/12 est bor-n^^e9 e sur toute bande $[]$ [] [251] Overfull \hbox (14.54329pt too wide) in paragraph at lines 4836--4840 []\T1/ptm/b/it/12 2. \T1/ptm/m/it/12 Prou-ver que si $\OML/cmm/m/it/12 z; w \OM S/cmsy/m/n/12 2 \U/msb/m/n/12 E$\T1/ptm/m/it/12 , $\OML/cmm/m/it/12 B [] \OT1/c mr/m/n/12 = []$\T1/ptm/m/it/12 , $\OML/cmm/m/it/12 B [] \OT1/cmr/m/n/12 = []\OM L/cmm/m/it/12 B []$ \T1/ptm/m/it/12 et $[] \U/msa/m/n/12 6 \OML/cmm/m/it/12 B [ ]$ [] Overfull \hbox (9.40994pt too wide) in paragraph at lines 4890--4894 []\T1/ptm/b/it/12 5. \T1/ptm/m/it/12 Prou-ver que $\OT1/cmr/m/n/12 ^^H[] [] = 0 $\T1/ptm/m/it/12 , $\OT1/cmr/m/n/12 ^^H [] = []$ \T1/ptm/m/it/12 et que pour to ut $\OML/cmm/m/it/12 x \OMS/cmsy/m/n/12 2 []$\T1/ptm/m/it/12 , $[][] \OT1/cmr/m /n/12 ^^H [][] \OML/cmm/m/it/12 dt \OT1/cmr/m/n/12 = 2 [][] ^^H [][] \OML/cmm/m /it/12 dt$\T1/ptm/m/it/12 . [] [252] [253]) (./Bergman.tex [254] 12. [255 ] Overfull \hbox (6.28609pt too wide) in paragraph at lines 200--214 \T1/ptm/m/n/12 existe $[][]\OML/cmm/m/it/12 ; :::; [][] \OMS/cmsy/m/n/12 2 \U/m sb/m/n/12 C$ \T1/ptm/m/n/12 tels que $[] [][]\OML/cmm/m/it/12 f[] \OT1/cmr/m/n/ 12 = 0$ \T1/ptm/m/n/12 sur $\OML/cmm/m/it/12 U$\T1/ptm/m/n/12 . En d^^e9-ri-van t, on ob-tient que $\OT1/cmr/m/n/12 ([] \OML/cmm/m/it/12 n[][]f[]\OT1/cmr/m/n/1 2 )\OML/cmm/m/it/12 f[] \OT1/cmr/m/n/12 = [] [256] LaTeX Font Warning: Command \small invalid in math mode on input line 264. [257] [258] [259] [260] [261] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 740. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `superscript' on input line 740. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\infty' on input line 740. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 740. [262] [263] [264] [265] [266] [267] [268]) (./SeriesFourier.tex [269] [270 ] 13. [271] [272] [273] [274] [275] [276] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 634. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `superscript' on input line 634. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 634. [277] Overfull \hbox (0.81068pt too wide) in paragraph at lines 721--731 []\T1/ptm/m/it/12 Soit $\OML/cmm/m/it/12 E$ \T1/ptm/m/it/12 un es-pace vec-to-r iel semi-norm^^e9 de fonc-tions d^^e9-fi-nies et Lebesgue-int^^e9grables [] [278] [279] [280] Overfull \hbox (10.20448pt too wide) in paragraph at lines 1117--1124 []\T1/ptm/b/n/12 Preuve. \T1/ptm/m/n/12 Si $\OML/cmm/m/it/12 r \OMS/cmsy/m/n/12 2 []$\T1/ptm/m/n/12 , la for-mule de Pois-son ap-pli-qu^^e9e ^^e0 la fonc-tion constante $\OT1/cmr/m/n/12 1$ \T1/ptm/m/n/12 donne $[][] \OML/cmm/m/it/12 p[] [] [] \OT1/cmr/m/n/12 = [] [281] [282] [283] [284] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 1483. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `superscript' on input line 1483. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\left' on input line 1483. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\right' on input line 1483. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 1483. [285] [286] [287] [288] [289] [290] [291] Overfull \hbox (52.801pt too wide) in paragraph at lines 2194--2208 \T1/ptm/m/n/12 Or la s^^e9-rie $\OT1/cmr/m/n/12 ([] [] [])$ \T1/ptm/m/n/12 con verge ab-so-lu-ment vers $\OT1/cmr/m/n/12 ^^C []$\T1/ptm/m/n/12 . Il en est don c de m^^eame de $\OT1/cmr/m/n/12 ([] [] [])$\T1/ptm/m/n/12 , [] [292] Overfull \hbox (6.35083pt too wide) in paragraph at lines 2325--2329 []\T1/ptm/m/it/12 D^^e9terminer toutes les formes li-n^^e9aires conti-nues $\OM L/cmm/m/it/12 F \OT1/cmr/m/n/12 : \OML/cmm/m/it/12 L[] [] \OMS/cmsy/m/n/12 ! \U /msb/m/n/12 C$ \T1/ptm/m/it/12 telles que $\OML/cmm/m/it/12 F [] \OT1/cmr/m/n/1 2 = [] Overfull \hbox (12.4316pt too wide) in paragraph at lines 2332--2334 []\T1/ptm/m/it/12 Pour $\OML/cmm/m/it/12 N \OMS/cmsy/m/n/12 2 \U/msb/m/n/12 N$\ T1/ptm/m/it/12 , on note $\OML/cmm/m/it/12 D[]$ \T1/ptm/m/it/12 le noyau de Di- ri-chlet d'ordre $\OML/cmm/m/it/12 N$ \T1/ptm/m/it/12 et on pose $\OML/cmm/m/it /12 F[] \OT1/cmr/m/n/12 = [] [][] \OML/cmm/m/it/12 D[]$ [] Overfull \hbox (40.77103pt too wide) in paragraph at lines 2335--2340 []\T1/ptm/b/it/12 a) \T1/ptm/m/it/12 Prou-ver que $\OML/cmm/m/it/12 F[] \OT1/cm r/m/n/12 = [][] [] [][]$ \T1/ptm/m/it/12 et que pour tout $\OML/cmm/m/it/12 t \ OMS/cmsy/m/n/12 2\OT1/cmr/m/n/12 ]0\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 2[][$\T1/ ptm/m/it/12 , $\OML/cmm/m/it/12 F[] [] \OT1/cmr/m/n/12 = [] [][]$\T1/ptm/m/it/1 2 . [] ) (./TransFourier.tex [293] [294 ] 14. [295] Overfull \hbox (19.00676pt too wide) in paragraph at lines 186--192 []\T1/ptm/m/it/12 Soient $\OML/cmm/m/it/12 E$ \T1/ptm/m/it/12 un $\OMS/cmsy/m/n /12 L[] []$\T1/ptm/m/it/12 -module et $[][]$ une unit^^e9 ap-pro-ch^^e9e sur $\ U/msb/m/n/12 R$ \T1/ptm/m/it/12 en $[][] \OMS/cmsy/m/n/12 2 []$\T1/ptm/m/it/12 . [] [296] [297] [298] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 459. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `superscript' on input line 459. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\left' on input line 459. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\right' on input line 459. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 459. [299] Overfull \hbox (13.97824pt too wide) in paragraph at lines 582--592 \T1/ptm/m/n/12 La for-mule ([]14.4[]) et le th^^e9o-r^^e8me de conver-gence do- mi-n^^e9e de Le-besgue livrent donc que $[] [] []$ [] Overfull \hbox (6.6461pt too wide) in paragraph at lines 625--634 \T1/ptm/m/it/12 lorsque $\OML/cmm/m/it/12 A$ \T1/ptm/m/it/12 tend vers $\OT1/cm r/m/n/12 +\OMS/cmsy/m/n/12 1$ \T1/ptm/m/it/12 des fonc-tions $\U/euf/m/n/12 F\O T1/cmr/bx/n/12 1[]\OML/cmm/m/it/12 f$\T1/ptm/m/it/12 , c'est ^^e0 dire des fonc -tions $[] \OMS/cmsy/m/n/12 7! [] [][] \OML/cmm/m/it/12 e[]f [] dx$\T1/ptm/m/it /12 . [] Overfull \hbox (24.90286pt too wide) in paragraph at lines 647--653 []\T1/ptm/m/it/12 Soient $\OML/cmm/m/it/12 a; b \OMS/cmsy/m/n/12 2 \U/msb/m/n/1 2 R$ \T1/ptm/m/it/12 tels que $\OML/cmm/m/it/12 a < b$\T1/ptm/m/it/12 . Alors $ \U/euf/m/n/12 F\OT1/cmr/bx/n/12 1[]$ \T1/ptm/m/it/12 est la fonc-tion $\OML/cmm /m/it/12 x \OMS/cmsy/m/n/12 7! [] [] [] \OML/cmm/m/it/12 e[]$\T1/ptm/m/it/12 . [] [300] [301] [302] [303] [304] Overfull \hbox (3.98137pt too wide) in paragraph at lines 1079--1083 []\T1/ptm/m/it/12 c) Soit $\OML/cmm/m/it/12 f \OT1/cmr/m/n/12 : []$ \T1/ptm/m/i t/12 une fonc-tion conti-nue et bor-n^^e9e. V^^e9-ri-fier que $\OML/cmm/m/it/12 G \OT1/cmr/m/n/12 : \U/msb/m/n/12 C \OMS/cmsy/m/n/12 3 \OML/cmm/m/it/12 z \OMS /cmsy/m/n/12 7! [][] \OML/cmm/m/it/12 e[]e[]f [] dx$ [] [305] [306]) (./Eqdiff.tex [307] [308 ] 15. [309] [310] [311] [312] [313] Overfull \hbox (3.10356pt too wide) in paragraph at lines 542--553 \OML/cmm/m/it/12 C[]$\T1/ptm/m/n/12 . Consi-d^^e9-rons la fonc-tion $\OML/cmm/m /it/12 G \OT1/cmr/m/n/12 = []$ \T1/ptm/m/n/12 o^^f9 $\OML/cmm/m/it/12 G[]$ \T1/ ptm/m/n/12 est la somme de la s^^e9-rie en-ti^^e8re $[]$. [] [314] Overfull \hbox (15.49396pt too wide) in paragraph at lines 626--633 \T1/ptm/m/n/12 On en d^^e9-duit que pour $\OML/cmm/m/it/12 s \OT1/cmr/m/n/12 = \OML/cmm/m/it/12 r []$\T1/ptm/m/n/12 , la fonc-tion $\OT1/cmr/m/n/12 ^^C : \OML /cmm/m/it/12 D [] \OMS/cmsy/m/n/12 3 \OML/cmm/m/it/12 z \OMS/cmsy/m/n/12 7! [] \OML/cmm/m/it/12 M [] []$ [] [315] [316] [317] [318] [319] [320] [321] [322] [323] [324] [325] [326] [327] [328] [329] [330] Overfull \hbox (1.92706pt too wide) in paragraph at lines 2238--2242 []\T1/ptm/m/it/12 Il n'existe pas de bi-ho-lo-mor-phisme entre le po-ly-disque unit^^e9 $\U/msb/m/n/12 D[] \OT1/cmr/m/n/12 = [] [331] [332] Overfull \hbox (12.99776pt too wide) in alignment at lines 2379--2392 [][][] [] [] [333] [334pdfTeX warning (ext4): destination with the same identifier (name{equ ation.15.7.47}) has been already used, duplicate ignored \AtBegShi@Output ...ipout \box \AtBeginShipoutBox \fi \fi l.2529 \textbf{3.} On suppose que $s_{2}-s_{1}\notin \mathbb{N}$. Prouver qu... pdfTeX warning (ext4): destination with the same identifier (name{equation.15.7 .47}) has been already used, duplicate ignored \AtBegShi@Output ...ipout \box \AtBeginShipoutBox \fi \fi l.2529 \textbf{3.} On suppose que $s_{2}-s_{1}\notin \mathbb{N}$. Prouver qu... ]pdfTeX warning (ext4): destination with the same identifier (name{equation.15. 7.47}) has been already used, duplicate ignored \relax l.2570 \begin{equation} pdfTeX warning (ext4): destination with the same identif ier (name{equation.15.7.47}) has been already used, duplicate ignored \relax l.2570 \begin{equation} pdfTeX warning (ext4): destination with the same identif ier (name{equation.15.7.47}) has been already used, duplicate ignored \relax l.2570 \begin{equation} pdfTeX warning (ext4): destination with the same identif ier (name{equation.15.7.47}) has been already used, duplicate ignored \relax l.2570 \begin{equation} pdfTeX warning (ext4): destination with the same identif ier (name{equation.15.7.47}) has been already used, duplicate ignored \relax l.2590 \begin{equation} pdfTeX warning (ext4): destination with the same identif ier (name{equation.15.7.47}) has been already used, duplicate ignored \relax l.2590 \begin{equation} pdfTeX warning (ext4): destination with the same identif ier (name{equation.15.7.47}) has been already used, duplicate ignored \relax l.2590 \begin{equation} pdfTeX warning (ext4): destination with the same identif ier (name{equation.15.7.47}) has been already used, duplicate ignored \relax l.2590 \begin{equation} [335] Overfull \hbox (8.29901pt too wide) in paragraph at lines 2685--2688 []\T1/ptm/b/it/12 a) \T1/ptm/m/it/12 Prou-ver que pour tout en-tier $\OML/cmm/m /it/12 n \OMS/cmsy/m/n/12 2 \U/msb/m/n/12 N$ \T1/ptm/m/it/12 et tout $\OML/cmm/ m/it/12 u; v \OMS/cmsy/m/n/12 2 \U/msb/m/n/12 C$\T1/ptm/m/it/12 , $\OML/cmm/m/i t/12 J[] [] \OT1/cmr/m/n/12 = [] \OML/cmm/m/it/12 J[] [] J[] []$\T1/ptm/m/it/12 . [] Overfull \hbox (15.01323pt too wide) in paragraph at lines 2708--2717 []\T1/ptm/m/it/12 On consi-d^^e8re le che-min (non born^^e9) [] [336] [337]) (./ZConstructionDeC.tex [338] Annexe A. [339 ] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 130. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 130. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 130. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `superscript' on input line 130. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 130. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 152. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 152. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 152. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\left' on input line 152. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\right' on input line 152. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 152. ) (./ZTopologie.tex [340] Annexe B. [341 ] [342] [343] [344] Overfull \hbox (3.72845pt too wide) in paragraph at lines 519--531 \T1/ptm/m/n/12 Soit $\OMS/cmsy/m/n/12 C$ \T1/ptm/m/n/12 une com-po-sante connex e de $\U/msb/m/n/12 S\OMS/cmsy/m/n/12 n\OML/cmm/m/it/12 K[]$\T1/ptm/m/n/12 . $\ OMS/cmsy/m/n/12 C$ \T1/ptm/m/n/12 ren-contre donc l'un des connexes $\U/msb/m/n /12 S\OMS/cmsy/m/n/12 n\OML/cmm/m/it/12 D []$ \T1/ptm/m/n/12 ou $\OML/cmm/m/it/ 12 D []$ [] [345] [346] [347] [348]) (./ZSimpleCnxJordan.tex [349] [350 ] Annexe C. [351] [352] File: C:/Users/VJM/Documents/Dropbox/3M266/Livre/graphics/LacetContractile__1.j pg Graphic file (type jpg) File: C:/Users/VJM/Documents/Dropbox/3M266/Livre/graphics/CerclesConcentriques_ _2.jpg Graphic file (type jpg) Underfull \vbox (badness 10000) has occurred while \output is active [] [353 ] [354 ] [355] [356] [357] [358] [359]) (./ZFamillesSommables.tex [360] Annexe D. Overfull \hbox (13.40215pt too wide) in paragraph at lines 41--47 \T1/ptm/m/n/12 Aussi a-t'on $\OML/cmm/m/it/12 a[] \OT1/cmr/m/n/12 = 0$ \T1/ptm/ m/n/12 pour $\OML/cmm/m/it/12 j [] K[]$\T1/ptm/m/n/12 . $\OML/cmm/m/it/12 K[]$ \T1/ptm/m/n/12 ^^e9tant une r^^e9union d^^e9-nom-brable d'en-semble fi-nis, $[] $ [] [361 ] [362] [363] [364]) (./ZCompactBord.tex [365] [366 ] Annexe E. Overfull \hbox (0.55984pt too wide) in paragraph at lines 61--73 []\T1/ptm/m/n/12 Un as-pect im-por-tant des com-pacts ^^e0 bord est qu'ils ad-m ettent des tan-gentes ou des demies-tangentes [] [367] [368] Overfull \hbox (13.92422pt too wide) in paragraph at lines 297--304 []\T1/ptm/m/it/12 3) Lorsque $\OML/cmm/m/it/12 a \OMS/cmsy/m/n/12 2 [] \OML/cmm /m/it/12 bK$ \T1/ptm/m/it/12 et $[]$ v^^e9-ri-fie (3), pour $\OML/cmm/m/it/12 x \OMS/cmsy/m/n/12 2 \U/msb/m/n/12 R[]$ \T1/ptm/m/it/12 et $\OT1/cmr/m/n/12 0 \O ML/cmm/m/it/12 < [] << \OT1/cmr/m/n/12 1$\T1/ptm/m/it/12 , les points $\OML/cmm /m/it/12 a \OMS/cmsy/m/n/12 ^^F [] []$\T1/ptm/m/it/12 , [] [369] [370] [371] Overfull \hbox (1.72339pt too wide) in paragraph at lines 675--678 []\T1/ptm/m/n/12 Les no-ta-tions sui-vantes sont utiles dans la th^^e9o-rie de l'in-t^^e9-gra-tion des formes dif-f^^e9-ren-tielles. Lorsque [] [372] [373] [374] [375] Underfull \vbox (badness 10000) has occurred while \output is active [] [376] Overfull \hbox (1.4761pt too wide) in paragraph at lines 1139--1143 []\T1/ptm/m/it/12 (5) Po-sant $[] \OT1/cmr/m/n/12 = []$ \T1/ptm/m/it/12 et no-t ant $[] []$ la fonc-tion qui ^^e0 $\OML/cmm/m/it/12 z \OMS/cmsy/m/n/12 2 \U/msb /m/n/12 C\OMS/cmsy/m/n/12 n\OML/cmm/m/it/12 bL$ \T1/ptm/m/it/12 as-so-cie $[] [ ] []$, [] [377] [378] File: C:/Users/VJM/Documents/Dropbox/3M266/Livre/graphics/Lacet__1.jpg Graphic file (type jpg) [379 ] [380] [381] [382] Underfull \hbox (badness 10000) in paragraph at lines 1819--1832 [] Overfull \hbox (17.40816pt too wide) in paragraph at lines 1833--1837 []\T1/ptm/m/n/12 (H) $[]$ ne contient pas de r^^e9el $[]$ tel que $[] [] \OT1/c mr/m/n/12 + \U/msb/m/n/12 R[][][] \OMS/cmsy/m/n/12 \ \OML/cmm/m/it/12 X \OT1/cm r/m/n/12 = \U/msb/m/n/12 ?$ \T1/ptm/m/n/12 lorsque $\OML/cmm/m/it/12 t \OMS/cms y/m/n/12 2 [] n []$\T1/ptm/m/n/12 . [] [383] [384] Overfull \hbox (1.92772pt too wide) in paragraph at lines 2135--2148 \T1/ptm/m/n/12 lorsque $\OML/cmm/m/it/12 Y \OMS/cmsy/m/n/12 2 C [] n []$\T1/ptm /m/n/12 , on ob-tient que $[] [] \OT1/cmr/m/n/12 = 0$ \T1/ptm/m/n/12 sur $\OML/ cmm/m/it/12 G[]$ \T1/ptm/m/n/12 pour tout $\OML/cmm/m/it/12 Y \OMS/cmsy/m/n/12 2 C [] n []$\T1/ptm/m/n/12 . [] [385] [386] [387]) Overfull \hbox (2.50406pt too wide) in paragraph at lines 2392--214 [][] \OML/cmm/m/it/12 > \OT1/cmr/m/n/12 0$ \T1/ptm/m/n/12 est tel que $[] \OMS/ cmsy/m/n/12 ^^Z \OML/cmm/m/it/12 V$\T1/ptm/m/n/12 . Gr^^e2ce ^^e0 l'as-ser-tion (3), on sait en par-ti-cu-lier que $\OML/cmm/m/it/12 p[] [] \OT1/cmr/m/n/12 = [] (./ZFormesDifferentielles.tex [388] Annexe F. Overfull \hbox (5.71959pt too wide) in paragraph at lines 36--43 $\OT1/cmr/m/n/12 ^^C[]\U/msb/m/n/12 C$ \T1/ptm/m/n/12 est l'es-pace des formes $\U/msb/m/n/12 C$\T1/ptm/m/n/12 -lin^^e9aires de $\U/msb/m/n/12 C$ \T1/ptm/m/n/ 12 dans $\U/msb/m/n/12 C$ \T1/ptm/m/n/12 et $\OT1/cmr/m/n/12 ^^C[]\U/msb/m/n/12 C$ \T1/ptm/m/n/12 est ce-lui des ap-pli-ca-tions $\U/msb/m/n/12 C$\T1/ptm/m/n/ 12 -antilin^^e9aires [] [389 ] [390] [391] [392]) (./ZIntegration.tex [393] [394 ] Annexe G. [395] [396] [397] [398] [399] Overfull \hbox (7.34428pt too wide) in paragraph at lines 570--578 []\T1/ptm/m/it/12 Soit $\OML/cmm/m/it/12 K$ \T1/ptm/m/it/12 un com-pact ^^e0 bo rd. On sup-pose que $[][]$ et $[][]$ [] [400] [401] [402] [403] [404] [405] Overfull \hbox (1.0118pt too wide) in paragraph at lines 1127--1131 []\T1/ptm/m/it/12 2) Une 1-forme dif-f^^e9-ren-tielle $[]$ sur $\OML/cmm/m/it/1 2 U$ \T1/ptm/m/it/12 est dite exacte s'il existe une fonc-tion $\OML/cmm/m/it/1 2 f$ \T1/ptm/m/it/12 qui est $\U/msb/m/n/12 R$\T1/ptm/m/it/12 -diff^^e9rentiabl e [] [406] [407]) (./swp0000.ind [408] Overfull \hbox (3.27782pt too wide) in paragraph at lines 25--27 []\T1/ptm/m/n/12 Cauchy-Riemann, op^^e9-ra-teur et ^^e9qua-tions de, []23[], [] [409 ] Overfull \hbox (8.4015pt too wide) in paragraph at lines 225--226 []\T1/ptm/m/n/12 principe d'uni-cite d'un pro-lon-ge-ment ana-ly-tique, [] [410] Overfull \hbox (2.03004pt too wide) in paragraph at lines 236--237 []\T1/ptm/m/n/12 prolongement ho-lo-morphe le long d'un che-min, [] Overfull \hbox (3.45709pt too wide) in paragraph at lines 289--291 []\T1/ptm/m/n/12 th^^e9or^^e8me de ca-rac-t^^e9-ri-sa-tion de l'exis-tence d'un e [] [411] Overfull \hbox (2.7496pt too wide) in paragraph at lines 343--345 []\T1/ptm/m/n/12 th^^e9or^^e8me de Weiers-trass sur la conver-gence uni- [] [412 ]) (./ZNotations.tex Annexe H. 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