ETH Zurich
E-Periodica
All volumes

L'Enseignement Mathématique

Volume 28 (1982)
Issue 1-2: L'ENSEIGNEMENT MATHÉMATIQUE
Front matter
Table of Contents
Front matter
Index
Front matter
Article: FROBENIUS RECIPROCITY AND LIE GROUP REPRESENTATIONS ON $\bar{\delta}$ COHOMOLOGY SPACES 3
Chapter: 1. Introduction 3
Chapter: 2. Induction and reciprocity 6
Chapter: 3. Representations of non-compact semisimple groups 15
Chapter: 4. Remarks on the nilpotent case: polarizations and harmonic induction 21
Chapter: 5. FURTHER NOTES 24
Bibliography 26
Article: ON THE NUMBER OF RESTRICTED PRIME FACTORS OF AN INTEGER. III 31
Chapter: §1. Introduction 31
Chapter: §2. Notation 37
Chapter: §3. Proofs of Theorems 1.6 and 1.11, and related results 38
Chapter: §4. Proofs of Theorem 1.14 and related results 43
Chapter: §5. Proofs of Theorem 1.21 and related results 46
Bibliography 51
Article: THE REPRESENTATION THEORY OF SL(2, R), A NON-INFINITESIMAL APPROACH 53
Abstract: Abstract 53
Chapter: 1. Introduction 53
Chapter: 2. The canonical matrix elements of the principal series 55
Chapter: 2.1. Preliminaries 55
Chapter: 2.2. The principal series 56
Chapter: 2.3. CALCULATION OF THE CANONICAL MATRIX ELEMENTS 58
Chapter: 2.4. Notes 60
Chapter: 3. The irreducible subquotient representations of the principal series 61
Chapter: 3.1. Subquotient representations 61
Chapter: 3.2. The case SU(1, 1) 63
Chapter: 3.3. Notes 65
Chapter: 4. Equivalences between irreducible subquotient representations OF THE PRINCIPAL SERIES 66
Chapter: 4.1. Naimark equivalence 66
Chapter: 4.2. The case SU(1, 1) 70
Chapter: 4.3. Notes 72
Chapter: 5. Equivalence of irreducible representations of SU(1, 1) to subrepresentations of the principal series 73
Chapter: 5.1. Spherical functions 73
Chapter: 5.2. Spherical functions of type δ 74
Chapter: 5.3. The generalized Abel transform 75
Chapter: 5.4. The main theorem 77
Chapter: 5.5. COMPLETION OF THE PROOF OF THE MAIN THEOREM 78
Chapter: 5.6. Notes 82
Chapter: 6. Unitarizability of irreducible subrepresentations OF THE PRINCIPAL SERIES 83
Chapter: 6.1. A CRITERIUM FOR UNITARIZABILITY 83
Chapter: 6.2. The case SU(1, 1) 85
Chapter: 6.3. Notes 87
Bibliography 88
Article: INTRODUCTION AUX VARIÉTÉS ABÉLIENNES COMPLEXES 91
Chapter: Intentions 91
Chapter: 1. Enoncé du théorème de base 92
Chapter: 2. Partie analytique de la démonstration 95
Chapter: 3. Commentaires concernant la partie analytique de la démonstration 107
Chapter: 4. Partie cohomologique de la démonstration 112
Chapter: 5. Commentaires concernant la partie cohomologique de la démonstration 121
Chapter: 6. Classification de variétés abéliennes 123
Bibliography 137
Article: UNE PRÉSENTATION ADÉLIQUE DE LA SÉRIE SINGULIÈRE ET DU PROBLÈME DE WARING 139
Chapter: Introduction 139
Chapter: Chapitre I. La transformation de Gauss 140
Chapter: Chapitre II. Le théorème de Hardy-Littlewood 154
Bibliography 170
Article: STRUCTURED vs GENERAL MODELS IN COMPUTATIONAL COMPLEXITY 171
Chapter: I. Introduction and Conclusion 171
Chapter: II. Comparison Based Models 175
Chapter: III. Arithmetic Models — Algebraic Complexity 181
Chapter: IV. Other Structured Models 184
Bibliography 187
Article: TURING MACHINES THAT TAKE ADVICE 191
Chapter: 1. Introduction 191
Chapter: 2. NONUNIFORM COMPLEXITY MEASURES 192
Chapter: 3. SUMMARY OF MAIN RESULTS 194
Chapter: 4. The Round-Robin Tournament Method 195
Chapter: 5. The Self-Reducibility Method 200
Chapter: 6. The Method of Recursive Definition 203
Bibliography 208
Article: NON-STANDARD MODELS OF PEANO ARITHMETIC 211
Chapter: II. Bounded Ultrapowers 213
Chapter: III. Peano arithmetic and the Stability Condition 218
Chapter: IV. Ramsey-type Theorems 222
Chapter: V. Construction of the Model 223
Chapter: VI. A Simpler Model 225
Chapter: VII. Variations 228
Chapter: Note (Added in proof) 230
Bibliography 231
Article: ON BOOLEAN ALGEBRAS WITH DISTINGUISHED SUBALGEBRAS 233
Chapter: 1. The sheaf representation of Boolean algebra extensions 235
Chapter: 2. Relative automorphisms of finite extensions 237
Chapter: 3. Truth values in for statements about (B, A) 242
Chapter: 4. Decidability and complétions of Th (K) 244
Bibliography 252
Article: RFDUCIBILITY BY ALGEBRAIC PROJECTIONS 253
Abstract: Abstract 253
Chapter: 1. Introduction 253
Chapter: 2. Definitions 254
Chapter: 3. p-DEFINABILITY 257
Chapter: 4. Closure properties 259
Chapter: 5. A NON-EXISTENT HIERARCHY 262
Chapter: 6. Universality of Linear Programming 263
Appendix: Appendix 1 265
Appendix: Appendix 2 267
Bibliography 268
Article: EINIGE UNENTSCHEIDBARE KÖRPERTHEORIEN 269
Preface: 0) EINLEITUNG 269
Chapter: 1) DISKUSSION DES RESULTATS 269
Chapter: 2) KONSTRUKTION VON M 272
Chapter: 3) KONSTRUKTION VON K 273
Chapter: 4) Die Eigenschaften von K 277
Chapter: 5) Beweis des Satzes 279
Bibliography 279
Article: MEILLEURE APPROXIMATION LINÉAIRE ET ESPACES EUCLIDIENS 281
Chapter: Introduction 281
Chapter: 1. Théorème principal, diverses formulations 281
Chapter: 2. DÉMONSTRATION DE LA DIFFÉRENTIABILITÉ 285
Chapter: 3. DÉMONSTRATION DU THÉORÈME A (CAS DIFFÉRENTIABLE) 290
Bibliography 293
Article: HARMONIZABLE PROCESSES: STRUCTURE THEORY 295
Abstract: Contents 295
Chapter: 1. Introduction 295
Chapter: 2. Harmonizability 300
Chapter: 3. Integral representation of a class of second order processes 305
Chapter: 4. V-BOUNDEDNESS, WEAK AND STRONG HARMONIZABILITY 314
Chapter: 5. Domination problem for harmonizable fields 322
Chapter: 6. Stationary dilations 326
Chapter: 7. Characterizations of weak harmonizability 332
Chapter: 8. Associated spectra and consequences 337
Chapter: 9. Multivariate extension and related problems 343
Bibliography 350
Rubric: BULLETIN BIBLIOGRAPHIQUE 1
Rubric: BULLETIN BIBLIOGRAPHIQUE 45
Back matter