Classical and modern methods in summability:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford Univ. Press
2000
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| Ausgabe: | 1. publ. |
| Schriftenreihe: | Oxford mathematical monographs
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 586 S. |
| ISBN: | 019850165X |
Internformat
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Datensatz im Suchindex
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| adam_text | CLASSICAL AND MODERN METHODS IN SUMMABILITY JOHANN BOOS FACHBEREICH
MATHEMATIK FERN UNIVERSITDT- GESAMTHOCHSCHULE HAGEN, GERMANY ASSISTED BY
PETER CASS DEPARTMENT OF MATHEMATICS THE UNIVERSITY OF WESTERN ONTARIO
LONDON, ONTARIO, CANADA OXFORD UNIVERSITY PRESS CONTENTS PART I
CLASSICAL METHODS IN SUMMABILITY AND APPLICATIONS CONVERGENCE AND
DIVERGENCE 3 1.1 THE EARLY HISTORY OF SUMMABILITY*THE DEVIL S IN-
VENTION 3 1.2 SUMMABILITY METHODS: DEFINITION AND EXAMPLES 5 1.3
QUESTIONS AND BASIC NOTIONS 20 1.4 NOTES ON CHAPTER 1 25 MATRIX METHODS:
BASIC CLASSICAL THEORY 26 2.1 DEALING WITH INFINITE SERIES 27 2.2
DEALING WITH INFINITE MATRICES 34 2.3 CONSERVATIVE MATRIX METHODS V 39
2.4 COERCIVE AND STRONGLY CONSERVATIVE MATRIX METHODS 51 2.5 ABUNDANCE
WITHIN DOMAINS; FACTOR SEQUENCES 61 2.6 COMPARISON AND CONSISTENCY
THEOREMS 75 2.7 TRIANGLES OF TYPE M 82 2.8 THE MEAN VALUE PROPERTY 87
2.9 POTENT MATRIX METHODS 92 2.10 NOTES ON CHAPTER 2 97 SPECIAL
SUMMABILITY METHODS 99 3.1 CESARO AND HOLDER METHODS 100 3.2 WEIGHTED
MEANS, RIESZ METHODS 112 3.3 NQRLUND METHODS 126 3.4 HAUSDORFF METHODS
136 3.5 METHODS OF FUNCTION THEORETICAL TYPE 152 3.6 SUMMABILITY METHODS
DEFINED BY POWER SERIES 157 3.7 NOTES ON CHAPTER 3 165 TAUBERIAN
THEOREMS 167 4.1 TAUBERIAN THEOREMS FOR CESARO METHODS 168 4.2 TAUBERIAN
THEOREMS, FOR RIESZ METHODS 178 4.3 TAUBERIAN THEOREMS FOR POWER SERIES
METHODS 186 4.4 HARDY-LITTLEWOOD S O-THEOREMS FOR THE ABEL METHOD 191
XII CONTENTS 4.5 HARDY-LITTLEWOOD S )-THEOREM FOR THE BOREL METHOD 196
4.6 NOTES ON CHAPTER 4 204 5 APPLICATION OF MATRIX METHODS 205 5.1
BOUNDARY BEHAVIOUR OF POWER SERIES 206 5.2 ANALYTIC CONTINUATION 214 5.3
NUMERICAL SOLUTION OF SYSTEMS OF LINEAR EQUATIONS 228 5.4 FOURIER
EFFECTIVENESS OF MATRIX METHODS 244 5.5 NOTES ON CHAPTER 5 256 PART II
FUNCTIONAL ANALYTIC METHODS IN SUMMABILITY 6 FUNCTIONAL ANALYTIC BASIS
261 6.1 TOPOLOGICAL SPACES 262 6.2 SEMI-METRIC SPACES 268 6.3
SEMI-NORMED SPACES, BANACH SPACES 280 6.4 LOCALLY CONVEX SPACES 292 6.5
CONTINUOUS LINEAR MAPS AND THE DUAL SPACE OF A LOCALLY CONVEX SPACE 306
6.6 DUAL PAIRS AND COMPATIBLE TOPOLOGIES 314 6.7 FRECHET SPACES 327 6.8
BARRELLED SPACES 335 7 TOPOLOGICAL SEQUENCE SPACES: K- AND FK-SPACES .
338 7.1 SEQUENCE SPACES AND THEIR -DUALS 339 _7.2 K-SPACES 349 7.3
FK-SPACES 359 7.4 FUNCTIONAL ANALYTIC PROOFS OF SOME TOEPLITZ-
SILVERMAN-TYPE THEOREMS 368 ___ - 7.5 THE DUAL OF FK-SPACES 375 7.6
DISTINGUISHED SUBSPACES OF FK-SPACES 385 7.7 NOTES ON CHAPTER 7 393 8
MATRIX METHODS: STRUCTURE OF THE DOMAINS 396 . 8.1 DOMAINS OF MATRIX
METHODS.AS FK-SPACES 397 8.2 DISTINGUISHED SUBSPACES OF DOMAINS 406 8.3
REPLACEABILITY AND /^-UNIQUENESS OF MATRICES 419 8.4 EXAMPLES 423 8.5
BOUNDED DIVERGENT SEQUENCES IN THE DOMAIN 438 8.6 CONSISTENCY AND
PERFECTNESS 443 8.7 REPLACEABILITY-AND INVARIANCE 448 8.8 NOTES ON
CHAPTER 8 454 CONTENTS XIII PART III COMBINING CLASSICAL AND FUNCTIONAL
ANALYTIC METHODS 9 CONSISTENCY OF MATRIX METHODS 459 9.1 CONSISTENCY AND
THEOREMS OF MAZUR-ORLICZ TYPE 460 9.2 //-BOUNDED SEQUENCES AND DOMAINS
475 9.3 /^-CONSISTENCY AND //-COMPARISON 483 9.4 SINGULARITIES OF
MATRICES 500 10 SAKS SPACES AND BOUNDED DOMAINS 515 10.1 SAKS SPACES AND
MIXED TOPOLOGIES 516 10.2 THE SAKS SPACE MNW E 522 10.3 A THEOREM OF
MAZUR-ORLICZ TYPE 527 10.4 6-COMPARISON THROUGH QUOTIENT REPRESENTATIONS
529 10.5 NOTES ON CHAPTER 10 536 11 SOME ASPECTS OF TOPOLOGICAL SEQUENCE
SPACES 538 11.1 AN INCLUSION THEOREM 538 11.2 GLIDING HUMP AND
OSCILLATING PROPERTIES 540 11.3 THEOREMS OF TOEPLITZ-SILVERMAN TYPE VIA
SECTIONAL CONVERGENCE AND ... 546 11.4 BARRELLED K-SPACES 550 11.5 THE
SEQUENCES OF ZEROS AND ONES IN A SEQUENCE SPACE 557 11.6 NOTES ON
CHAPTERS 9 AND 11 561 BIBLIOGRAPHY 563 INDEX 575
|
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| discipline | Mathematik |
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| indexdate | 2024-07-09T19:04:48Z |
| institution | BVB |
| isbn | 019850165X |
| language | English |
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| physical | XIII, 586 S. |
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| spelling | Boos, Johann 1944- Verfasser (DE-588)1012994589 aut Classical and modern methods in summability Johann Boos ; assisted by Peter Cass 1. publ. Oxford Oxford Univ. Press 2000 XIII, 586 S. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Functionaalanalyse gtt Summability theory Summierbarkeit (DE-588)4294383-8 gnd rswk-swf Summierbarkeit (DE-588)4294383-8 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009950057&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Boos, Johann 1944- Classical and modern methods in summability Functionaalanalyse gtt Summability theory Summierbarkeit (DE-588)4294383-8 gnd |
| subject_GND | (DE-588)4294383-8 |
| title | Classical and modern methods in summability |
| title_auth | Classical and modern methods in summability |
| title_exact_search | Classical and modern methods in summability |
| title_full | Classical and modern methods in summability Johann Boos ; assisted by Peter Cass |
| title_fullStr | Classical and modern methods in summability Johann Boos ; assisted by Peter Cass |
| title_full_unstemmed | Classical and modern methods in summability Johann Boos ; assisted by Peter Cass |
| title_short | Classical and modern methods in summability |
| title_sort | classical and modern methods in summability |
| topic | Functionaalanalyse gtt Summability theory Summierbarkeit (DE-588)4294383-8 gnd |
| topic_facet | Functionaalanalyse Summability theory Summierbarkeit |
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