Analysis I

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Springer Science & Business Media, 2004 - Mathematics - 430 pages
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Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas over calculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first two volumes are now available in English.

 

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Contents

II
1
III
7
IV
10
V
13
VI
17
VII
19
VIII
23
IX
25
XLIX
234
L
239
LI
241
LII
244
LIII
252
LIV
260
LV
265
LVI
270

X
28
XI
31
XII
39
XIII
45
XV
53
XVI
56
XVII
59
XVIII
63
XIX
67
XX
76
XXI
81
XXII
95
XXIII
98
XXIV
103
XXV
110
XXVI
114
XXVII
119
XXVIII
123
XXIX
127
XXX
132
XXXI
138
XXXII
139
XXXIII
148
XXXIV
158
XXXV
162
XXXVI
167
XXXVII
178
XXXVIII
187
XL
192
XLI
197
XLII
200
XLIII
205
XLIV
211
XLV
216
XLVI
220
XLVII
225
XLVIII
228
LVII
273
LIX
276
LX
279
LXI
284
LXII
287
LXIII
290
LXIV
303
LXV
306
LXVI
308
LXVII
311
LXVIII
313
LXIX
316
LXX
320
LXXI
322
LXXII
325
LXXIV
327
LXXV
330
LXXVI
332
LXXVII
333
LXXVIII
336
LXXIX
339
LXXX
342
LXXXI
345
LXXXII
346
LXXXIII
351
LXXXIV
359
LXXXV
368
LXXXVI
372
LXXXVII
383
LXXXVIII
388
LXXXIX
394
XC
397
XCI
403
XCII
407
XCIII
414
XCIV
425
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About the author (2004)

Roger Godement (October 1, 1921 - July 21, 2016) is known for his work in functional analysis, and also his expository books. He started as a student at the cole normale sup rieure in 1940, where he became a student of Henri Cartan. He started research into harmonic analysis on locally compact abelian groups, finding a number of major results; this work was in parallel but independent of similar investigations in the USSR and Japan. Work on the abstract theory of spherical functions published in 1952 proved very influential in subsequent work, particularly that of Harish-Chandra. The isolation of the concept of square-integrable representation is attributed to him. The Godement compactness criterion in the theory of arithmetic groups was a conjecture of his. He later worked with Jacquet on the zeta function of a simple algebra. He was an active member of the Bourbaki group in the early 1950s, and subsequently gave a number of significant Bourbaki seminars. He also took part in the Cartan seminar. He also wrote texts on Lie groups, abstract algebra and mathematical analysis.