Holdings: Mathematical analysis during the 20th century

Mathematical analysis during the 20th century:

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Bibliographic Details
Main Author:	Pier, Jean-Paul (Author)
Format:	Book
Language:	English
Published:	Oxford [u.a.] Oxford Univ. Press 2001
Edition:	1. publ.
Subjects:	Geschichte 1900-2000 Analyse (wiskunde) Analyse mathématique - Histoire - 20e siècle Geschichte Mathematical analysis > History > 20th century Analysis
Online Access:	Inhaltsverzeichnis
Physical Description:	X, 428 S.
ISBN:	0198503946

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MARC


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Record in the Search Index

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adam_text	MATHEMATICAL ANALYSIS DURING THE 20TH CENTURY JEAN-PAUL PIER CENTRE UNIVERSITAIRE DE LUXEMBOURG OXFORD UNIVERSITY PRESS CONTENTS 1 INTRODUCTION 1 1.1 THE SCOPE OF ANALYSIS 2 1.1.1 THE GREAT CLASSICS ON ANALYSIS 2 1.1.2 THE CHANGING OBJECT OF ANALYSIS 4 1.2 MAIN STREAMS IN A TURBULENT ACTIVITY 12 1.2.1 THE QUESTION OF SUBDIVIDING MATHEMATICAL ANALYSIS 12 1.2.2 HOW TO ORGANIZE THE SUBJECT 16 2 GENERAL TOPOLOGY 27 2.1 EVOLUTION 1900-1950 27 2.1.1 TOPOLOGICAL AXIOMATIZATIONS 27 2.1.2 TOPOLOGICAL ALGEBRA 37 2.1.3 FILIATIONS 40 2.1.4 DIMENSION THEORY 42 2.1.5 COMPLEMENTARY INPUTS 42 2.2 FLASHES 1950-2000 44 2.2.1 AN ACCOMPLISHED SUBJECT 44 2.2.2 GENERALIZED TOPOLOGICAL CONCEPTS 45 3 INTEGRATION AND MEASURE 47 3.1 EVOLUTION 1900-1950 47 3.1.1 LEBESGUE INTEGRATION 47 3.1.2 THE GENERAL CONCEPT OF MEASURE 55 3.1.3 PARADOXICAL DECOMPOSITION 61 3.1.4 PERIOD OF CONSOLIDATION 61 3.2 FLASHES 1950-2000 63 3.2.1 STANDING PROBLEMS 63 3.2.2 ABSTRACT FORMULATIONS 64 3.2.3 GENERALIZED RIEMANN INTEGRALS 68 3.2.4 OUTLOOK 69 4 FUNCTIONAL ANALYSIS 73 4.1 EVOLUTION 1900-1950 73 4.1.1 NEW OBJECTIVES 73 4.1.2 THEORY OF INTEGRAL EQUATIONS 79 4.1.3 BANACH SPACES 86 4.1.4 HILBERT SPACES 92 CONTENTS 4.1.5 VON NEUMANN ALGEBRAS 95 4.1.6 BANACH ALGEBRAS 98 4.1.7 DISTRIBUTIONS 101 4.2 FLASHES 1950-2000 106 4.2.1 TOPOLOGICAL VECTOR SPACES 106 4.2.2 EXTENSION OF WEIERSTRAG S THEOREM 108 4.2.3 FRECHET SPACES, SCHWARTZ SPACES, SOBOLEV SPACES 108 4.2.4 BANACH SPACE PROPERTIES 110 4.2.5 HILBERT SPACE PROPERTIES 113 4.2.6 BANACH ALGEBRA AND C*-ALGEBRA PROPERTIES 114 4.2.7 APPROXIMATION PROPERTIES 117 4.2.8 NUCLEARITY 117 4.2.9 VON NEUMANN ALGEBRA PROPERTIES 123 4.2.10 SPECIFIC TOPICS 126 5 HARMONIC ANALYSIS 129 5.1 EVOLUTION 1900-1950 129 5.1.1 FOURIER SERIES 129 5.1.2 INVARIANT MEASURES 137 5.1.3 ALMOST PERIODIC FUNCTIONS 140 5.1.4 UNIQUENESS OF INVARIANT MEASURES 141 5.1.5 CONVOLUTIONS 142 5.1.6 AN EVOLUTION LINKED TO THE HISTORY OF PHYSICS 145 5.1.7 REPRESENTATION THEORY 150 5.1.8 STRUCTURAL PROPERTIES OF TOPOLOGICAL GROUPS 154 5.7.9 POSITIVE-DEFINITE FUNCTIONS 155 5.1.10 HARMONIC SYNTHESIS 157 5.1.11 METRIC LOCALLY COMPACT ABELIAN GROUPS 160 5.2 FLASHES 1950-2000 163 5.2.1 FOURIER TRANSFORMS 163 5.2.2 CONVOLUTION PROPERTIES 166 5.2.3 GROUP REPRESENTATIONS 166 5.2.4 REMARKABLE BANACH ALGEBRAS OF FUNCTIONS ON A LOCALLY COMPACT GROUP 169 5.2.5 SPECIFIC SETS 170 5.2.6 SPECIFIC GROUPS 171 5.2.7 HARMONIC ANALYSIS ON SEMIGROUPS 173 5.2.8 WAVELETS 174 5.2.9 GENERALIZED ACTIONS 176 6 LIE GROUPS 179 6.1 EVOLUTION 1900-1950 179 6.1.1 LIE GROUPS AND LIE ALGEBRAS 179 6.1.2 SYMMETRIC RIEMANNIAN SPACES 185 6.1.3 HILBERT S PROBLEM FOR LIE GROUPS 187 6.1.4 REPRESENTATIONS OF LIE GROUPS 188 6.2 FLASHES 1950-2000 189 CONTENTS IX 6.2.1 6.2.2 6.2.3 6.2.4 6.2.5 THE WIDE RANGE OF LIE GROUP THEORY SOLUTION OF HILBERT S PROBLEM ON LIE GROUPS ERGODICITY PROBLEMS { SPECIFIC CLASSES OF LIE GROUPS EXTENSIONS OF LIE GROUP THEORY THEORY OF FUNCTIONS AND ANALYTIC GEOMETRY 7.1 7.2 EVOLUTION 1900-1950 7.1.1 7.1.2 7.1.3 7.1.4 FLASHES 7.2.1 7.2.2 7.2.3 7.2.4 ORDINARY AND 8.1 8.2 THE NINETEENTH CENTURY CONTINUED POTENTIAL THEORY CONFORMAL MAPPINGS TOWARDS A THEORY OF SEVERAL COMPLEX VARIABLES 1950-2000 ACCOMPLISHMENTS ON PREVIOUS TOPICS HARDY SPACES THE DOMINANCE OF THE THEORY OF SEVERAL COMPLEX VARI- ABLES ITERATION PROBLEMS PARTIAL DIFFERENTIAL EQUATIONS EVOLUTION 1900-1950 8.1.1 8.1.2 8.1.3 FLASHES 8.2.1 8.2.2 8.2.3 NEW TRENDS FOR CLASSICAL PROBLEMS FIXED POINT PROPERTIES FROM THE ORDINARY DIFFERENTIAL CASE TO THE PARTIAL DIFFER- ENTIAL CASE 1950-2000 DIFFERENTIAL EQUATIONS PARTIAL DIFFERENTIAL EQUATIONS TENTACULAR SUBJECTS ALGEBRAIC TOPOLOGY 9.1 9.2 EVOLUTION 1900-1950 9.1.1 9.1.2 9.1.3 9.1.4 8.1.3 9.1.5 FLASHES 9.2.1 9.2.2 THE ORIGINS OF ALGEBRAIC TOPOLOGY SIMPLICIAL THEORIES HOMOTOPY THEORY FIBRES AND FIBRATIONS FROM THE ORDINARY DIFFERENTIAL CASE TO THE PARTIAL DIFFER- ENTIAL CASE THE BREAKTHROUGHS DUE TO EILENBERG, MACLANE, AND LERAY 1950-2000 THE POWER OF THE MACHINERY GENERALIZATIONS 189 191 191 192 196 199 200 200 209 211 212 215 215 219 223 227 229 229 229 231 232 236 236 238 247 255 255 255 261 267 270 232 271 275 275 278 10 DIFFERENTIAL TOPOLOGY 280 10.1 EVOLUTION 1900-1950 280 10.1.1 THE BEGINNING OF THE CENTURY 280 10.1.2 E. CARTAN S WORK . 283 CONTENTS 10.1.3 10.1.4 10.1.5 10.1.6 10.1.7 10.1.8 10.2 FLASHES 10.2.1 10.2.2 10.2.3 10.2.4 10.2.5 11 PROBABILITY TENSOR PRODUCTS AND EXTERIOR DIFFERENTIALS MORSE THEORY WHITNEY S WORK DE RHAM S WORK HODGE THEORY THE FRAMING OF THE SUBJECT 1950-2000 THE STATUS OF DIFFERENTIABLE MANIFOLDS FOLIATIONS NEW OBJECTIVES FROM POINCARE S HERITAGE GLOBAL ANALYSIS 11.1 EVOLUTION 1900-1950 11.1.1 11.1.2 11.1.3 11.1.4 11.1.5 11.2 FLASHES 11.2.1 11.2.2 11.2.3 11.2.4 FIRST RESULTS BROWNIAN MOTION ERGODICITY PROBABILITIES AS MEASURES STOCHASTIC INTEGRALS 1950-2000 PROBABILITY THEORY, A PART OF ANALYSIS DYNAMICAL SYSTEMS AND ERGODICITY ENTROPY STOCHASTIC PROCESSES 12 ALGEBRAIC GEOMETRY 12.1 EVOLUTION 1900-1950 12.1.1 12.1.2 12.1.3 12.1.4 12.2 FLASHES 12.2.1 12.2.2 12.2.3 12.2.4 12.2.5 12.2.6 12.2.7 REFERENCES INDEX OF NAMES INDEX OF TERMS ALGEBRAIC GEOMETRY AND NUMBER THEORY THE MORDELL CONJECTURE TRANSCENDENCE AND PRIME NUMBERS THE RIEMANN CONJECTURE 1950-2000 ARITHMETICAL PROPERTIES INVESTIGATIONS ON TRANSCENDENTAL NUMBERS A CENTRAL OBJECT OF STUDY ETALE COHOMOLOGY THE GENERAL RIEMANN-ROCH THEOREMS IT-THEORY FURTHER STUDIES APPENDIX: LIST OF SYMBOLS 284 287 288 291 293 297 299 299 302 303 307 310 314 314 314 318 320 321 324 325 325 326 328 328 331 331 331 334 336 338 339 339 340 341 345 345 346 349 350 410 418 427
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author	Pier, Jean-Paul
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era_facet	Geschichte 1900-2000
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spelling	Pier, Jean-Paul Verfasser aut Mathematical analysis during the 20th century Jean-Paul Pier 1. publ. Oxford [u.a.] Oxford Univ. Press 2001 X, 428 S. txt rdacontent n rdamedia nc rdacarrier Geschichte 1900-2000 Geschichte 1900-2000 gnd rswk-swf Analyse (wiskunde) gtt Analyse mathématique - Histoire - 20e siècle Geschichte Mathematical analysis -- History -- 20th century Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s Geschichte 1900-2000 z DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009497161&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Pier, Jean-Paul Mathematical analysis during the 20th century Analyse (wiskunde) gtt Analyse mathématique - Histoire - 20e siècle Geschichte Mathematical analysis -- History -- 20th century Analysis (DE-588)4001865-9 gnd
subject_GND	(DE-588)4001865-9
title	Mathematical analysis during the 20th century
title_auth	Mathematical analysis during the 20th century
title_exact_search	Mathematical analysis during the 20th century
title_full	Mathematical analysis during the 20th century Jean-Paul Pier
title_fullStr	Mathematical analysis during the 20th century Jean-Paul Pier
title_full_unstemmed	Mathematical analysis during the 20th century Jean-Paul Pier
title_short	Mathematical analysis during the 20th century
title_sort	mathematical analysis during the 20th century
topic	Analyse (wiskunde) gtt Analyse mathématique - Histoire - 20e siècle Geschichte Mathematical analysis -- History -- 20th century Analysis (DE-588)4001865-9 gnd
topic_facet	Analyse (wiskunde) Analyse mathématique - Histoire - 20e siècle Geschichte Mathematical analysis -- History -- 20th century Analysis
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work_keys_str_mv	AT pierjeanpaul mathematicalanalysisduringthe20thcentury

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