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Issue 1: L'ENSEIGNEMENT MATHÉMATIQUE
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Front matter
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Table of Contents
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Front matter
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Index
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Front matter
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Article
ANALYTIC SPACES
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1
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Abstract
CONTENTS
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1
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Chapter
Chapter 1 ANALYTIC SPACES AND OPERATIONS ON THEM
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1
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Chapter
1.1 Reduced analytic spaces.
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2
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Chapter
1.2. Definition of general analytic spaces.
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3
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Chapter
1.3. Operations on analytic spaces.
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8
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Chapter
1.4. Relations between reduced and non-reduced spaces.
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10
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Chapter
Chapter 2. DIFFERENTIAL CALCULUS ON ANALYTIC SPACES
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11
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Chapter
Chapter 3. FINITE MORPHISMS
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16
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Chapter
3.1. Local theory.
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16
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Chapter
3.2. Germs of analytic spaces.
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20
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Chapter
3.3 Finite morphisms
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21
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Chapter
Chapter 4. THE FINITENESS THEOREM
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22
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Chapter
4.1. Stein spaces
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22
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Chapter
4.2. Topology on Γ(X, F).
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23
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Chapter
4.3. Topology on $H^p (X, F)$
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24
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Chapter
4.4. The finiteness theorem
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26
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Appendix
Appendix Local noetherian rings
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27
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Bibliography
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28
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Article
MEROMORPHIC MAPPINGS
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29
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Chapter
Introduction
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29
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Chapter
1. Correspondences
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29
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Chapter
2. HOLOMORPHIC CORRESPONDENCES
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32
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Chapter
3. Meromorphic mappings
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33
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Chapter
4. Extension of meromorphic mappings
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36
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Chapter
5. Maximal meromorphic mappings
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41
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Bibliography
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46
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Article
FLATNESS AND PRIVILEGE
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47
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Chapter
I. Flat Morphisms
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47
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Chapter
§1. Analytic subspaces of an analytic space
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47
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Chapter
§2. Analytic pull-back
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48
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Chapter
§3. Introduction to flatness by examples
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49
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Chapter
§4. Algebraic study of flatness
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51
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Chapter
§5. Geometrie applications of the flatness criterions
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58
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Chapter
III. Privileged polycylinders
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62
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Chapter
§1. Banach vector bundles over an analytic space
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62
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Chapter
§2. Privileged polycylinders
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66
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Chapter
IV. FLATNESS AND PRIVILEGE
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69
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Chapter
§1. Morphisms from an analytic space into B (K)
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69
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Chapter
§2. The flatness and privilege theorem
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70
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Bibliography
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74
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Article
COMPACT ANALYTICAL VARIETIES
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75
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Abstract
CONTENTS
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75
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Chapter
Introduction
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75
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Chapter
1. Preliminaries
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75
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Chapter
2. The vanishing theorem of Kodaira
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77
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Chapter
3. An imbedding theorem
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80
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Chapter
4. Line bundle associated to a divisor
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82
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Chapter
5. Meromorphic forms
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85
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Chapter
6. The Atiyah-Hodge theorem
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86
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Chapter
7. Lefschetz' theorem on hyperplane sections
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93
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Bibliography
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97
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Article
THE COHERENCE OF DIRECT IMAGES
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99
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Chapter
Introduction
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99
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Chapter
Cohomology theory
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99
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Chapter
Stein manifolds
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100
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Chapter
Direct images of sheaves
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101
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Chapter
VERY SPECIAL CASE
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102
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Chapter
Measure charts
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104
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Chapter
Existence of admissible refinements of measure coverings
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106
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Chapter
General Theory
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107
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Chapter
Smoothing
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109
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Chapter
Approximation
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114
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Chapter
Main Theorem
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117
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Bibliography
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119
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Article
REPRESENTATIONS OF COMPACT GROUPS AND SPHERICAL HARMONICS
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121
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Chapter
§1. Introductory Remarks
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121
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Chapter
§2. The construction of irreducible representations of some special groups
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126
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Chapter
§3. Representations of Class 1 and Spherical Harmonics
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140
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Chapter
§4. SOME PROPERTIES OF SPHERICAL HARMONICS
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150
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Chapter
§5. Special results for n=4
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164
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Chapter
§6. The Fourier transform of functions on $R^n$
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167
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Bibliography
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172
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Article
MULTIPLIERS OF UNIFORM CONVERGENCE
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175
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Bibliography
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187
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Article
UNE REMARQUE SUR ξ(1+it)
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189
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Rubric
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192
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Article
ON A PROBLEM OF ERDÖS
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193
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Bibliography
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193
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Rubric
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194
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Article
L'HYPOTHÈSE DE FERMAT POUR LES EXPOSANTS NÉGATIFS
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195
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Article
SOMMES DE PUISSANCES m iemes DANS LES ANNEAUX ß-ADIQUES ET LES ANNEAUX D'ENTIERS ALGÉBRIQUES
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197
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Chapter
1. Introduction
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197
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Chapter
2. Sommes de puissances m iemes dans un anneau ß-adique
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198
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Chapter
3. Sommes de puissances m iemes dans un anneau d'entiers algébriques
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199
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Chapter
4. DÉMONSTRATION DU THÉORÈME (3.3).
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201
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Bibliography
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204
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Article
SUR QUELQUES APPLICATIONS DE LA «MÉTHODE DE L'HYPERBOLE» DE DIRICHLET A LA THÉORIE DES NOMBRES PREMIERS
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205
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Chapter
I. Introduction
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205
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Chapter
II. Sur un théorème de Hardy et Ramanujan
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206
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Chapter
III. Sur un théorème de Rényi et Delange
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213
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Chapter
IV. MÉTHODE ANALYTIQUE
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222
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Appendix
Appendice
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222
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Bibliography
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224
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Article
SUR UNE CLASSE DE PROPRIÉTÉS COMMUNES A QUELQUES TYPES DIFFÉRENTS D'ALGÈBRES
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225
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Chapter
Introduction
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225
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Chapter
Partie I : Quelques types d'algèbres
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227
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Chapter
Partie II: Algèbres associatives et applications multilinéaires
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237
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Chapter
Partie III: Algèbres de Lie et algèbres de Vinberg — plus sur les déformations — systèmes de composition
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254
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Bibliography
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274
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Chapter
Notes bibliographiques concernant la partie I
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276
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Chapter
Notes bibliographiques de la partie II
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276
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Chapter
Notes bibliographiques de la partie III
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276
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Rubric
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278
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Article
CONTINUITY OF FUNCTIONS OF SEVERAL VARIABLES
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279
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Bibliography
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281
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Rubric
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282
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Article
EIN HOLOMORPH-SEPARABLER KOMPLEXER RAUM MUSS NICHT HOLOMORPH-REGULÄR SEIN
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283
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Notes
Bemerkungen
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284
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Bibliography
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284
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Article
NOTE ON ABSOLUTE SUMMABILITY FACTORS
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285
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Bibliography
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288
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Article
CONVEXITÉ ET ENCHAÎNEMENT
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289
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Bibliography
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302
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Article
CLASSES DE CHERN D'UN ESPACE HOMOGÈNE PRESQUE COMPLEXE
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303
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Chapter
1. Donnée du problème
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303
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Chapter
2. Extension des fibres principaux
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304
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Chapter
3. Interprétations des représentations complexes irréductibles d'un tore T
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307
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Chapter
4. Classes de Chern d'un fibré vectoriel complexe associé a un G-fibré principal
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310
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Chapter
5. Classe de Chern d'un espace homogène presque complexe
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311
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Chapter
Appendice: le principe de clivage
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313
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Bibliography
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315
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Rubric
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316
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Article
ADDENDUM ON SOME GENERALISATIONS OF ABEL SUMMABILITY
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317
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Bibliography
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319
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Chapter
ENQUÊTE DE LA COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (CONGRÈS INTERNATIONAL D'AMSTERDAM — 1954).
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331
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Rubric
COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (C.I.E.M.)
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332
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Rubric
SOCIÉTÉ MATHÉMATIQUE SUISSE
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335
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Rubric
BULLETIN BIBLIOGRAPHIQUE
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1
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Back matter
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8
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Rubric
BULLETIN BIBLIOGRAPHIQUE
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9
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Rubric
BULLETIN BIBLIOGRAPHIQUE
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23
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Back matter
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