Analysis in integer and fractional dimensions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2001
|
| Edition: | 1. publ. |
| Series: | Cambridge studies in advanced mathematics
71 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | MA0000485 |
| Physical Description: | XIX, 556 S. |
| ISBN: | 0521650844 |
Staff View
MARC
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Record in the Search Index
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| adam_text | ANALYSIS IN INTEGER AND FRACTIONAL DIMENSIONS RON BLEI UNIVERSITY OF
CONNECTICUT ^ *I UNIVERSITY PRE^S CONTENTS PREFACE XIII ACKNOWLEDGEMENTS
XIX I A PROLOGUE: MOSTLY HISTORICAL 1 1. FROM THE LINEAR TO THE BILINEAR
1 2. A BILINEAR THEORY 6 3. MORE OF THE BILINEAR 8 4. PROM BILINEAR TO
MULTILINEAR AND FRACTION-LINEAR 10 EXERCISES 15 HINTS FOR EXERCISES IN
CHAPTER I 18 II THREE CLASSICAL INEQUALITIES 19 1. MISE EN SCENE:
RADEMACHER FUNCTIONS 19 2. THE KHINTCHIN L 1 -!, 2 INEQUALITY 21 3. THE
LITTLEWOOD AND ORLICZ MIXED-NORM INEQUALITIES 23 4. THE THREE
INEQUALITIES ARE EQUIVALENT 25 5. AN APPLICATION: LITTLEWOOD S
4/3-INEQUALITY 26 6. GENERAL SYSTEMS AND BEST CONSTANTS 28 EXERCISES 31
HINTS FOR EXERCISES IN CHAPTER II 36 III A FOURTH INEQUALITY 38 1. MISE
EN SCENE: DOES THE KHINTCHIN L 1 -!, 2 INEQUALITY IMPLY THE GROTHENDIECK
INEQUALITY? 38 2. AN ELEMENTARY PROOF 40 3. A SECOND ELEMENTARY PROOF 43
4. A(2)-UNIFORMIZABILITY 46 5. A REPRESENTATION OF AN INNER PRODUCT IN A
HILBERT SPACE 51 6. COMMENTS (MAINLY HISTORICAL) AND LOOSE ENDS 53 VN
VIII CONTENTS EXERCISES 57 HINTS FOR EXERCISES IN CHAPTER III 58 IV
ELEMENTARY PROPERTIES OF THE FRECHET ~ VARIATION - AN INTRODUCTION TO
TENSOR PRODUCTS 60 1. MISE EN SCENE: THE SPACE F K (N,...,N) 60 2.
EXAMPLES 61 3. FINITELY SUPPORTED FUNCTIONS ARE NORM-DENSE IN F FE
(N,... ,N) 63 4. TWO CONSEQUENCES 67 5. THE SPACE V K (N, ... ,N) 72 6.
A BRIEF INTRODUCTION TO GENERAL TOPOLOGICAL TENSOR PRODUCTS 80 7. A
BRIEF INTRODUCTION TO PROJECTIVE TENSOR ALGEBRAS 82 8. A HISTORICAL
BACKDROP 86 EXERCISES 88 HINTS FOR EXERCISES IN CHAPTER IV 92 V THE
GROTHENDIECK FACTORIZATION THEOREM 95 1. MISE EN SCENE: FACTORIZATION IN
ONE DIMENSION 95 2. AN EXTENSION TO TWO DIMENSIONS 96 3. AN
APPLICATION 98 4. THE FF-NORM 100 5. THE G-NOTM IN THE MULTILINEAR CASE
103 EXERCISES 105 HINTS FOR EXERCISES IN CHAPTER V 106 VI AN
INTRODUCTION TO MULTIDIMENSIONAL MEASURE THEORY 107 1. MISE EN SCENE:
FRECHET MEASURES 107 2. EXAMPLES 108 3. THE FRECHET VARIATION ILL 4. AN
EXTENSION THEOREM 116 5. INTEGRALS WITH RESPECT TO F N -MEASURES 118 6.
THE PROJECTIVE TENSOR ALGEBRA V^CI,..., C N ) 121 7. A MULTILINEAR RIESZ
REPRESENTATION THEOREM 122 8. A HISTORICAL BACKDROP 126 EXERCISES 129
HINTS FOR EXERCISES IN CHAPTER VI 133 CONTENTS IX VII AN INTRODUCTION TO
HARMONIC ANALYSIS 135 1. MISE EN SCENE: MAINLY A HISTORICAL PERSPECTIVE
135 2. THE SETUP 138 3. ELEMENTARY REPRESENTATION THEORY 142 4. SOME
HISTORY 146 5. ANALYSIS OF WALSH SYSTEMS: A FIRST STEP 147 6. WK IS A
ROSENTHAL SET 151 7. RESTRICTION ALGEBRAS 157 8. HARMONIC ANALYSIS AND
TENSOR ANALYSIS 159 9. BONAMI S INEQUALITIES: A MEASUREMENT OF
COMPLEXITY 167 10. THE LITTLEWOOD 2N/(N + 1)-INEQUALITIES: ANOTHER
MEASUREMENT OF COMPLEXITY 175 11. P-SIDON SETS 181 12. TRANSCRIPTIONS
190 EXERCISES 196 HINTS FOR EXERCISES IN CHAPTER VII 202 VIII
MULTILINEAR EXTENSIONS OF THE GROTHENDIECK INEQUALITY (VIA
A(2)-UNIFORMIZABILITY) 206 1. MISE EN SCENE: A BASIC ISSUE 206 2.
PROJECTIVE BOUNDEDNESS , 208 3. UNIFORMIZABLE A(2)-SETS 209 4. A
PROJECTIVELY BOUNDED TRILINEAR FUNCTIONAL 214 5. A CHARACTERIZATION 221
6. PROJECTIVELY UNBOUNDED TRILINEAR FUNCTIONAL 225 7. THE GENERAL CASE
227 8. IF ~ 1 230 9. PROOF OF THEOREM 19 236 EXERCISES 242 * HINTS FOR
EXERCISES IN CHAPTER VIII 245 IX PRODUCT FRECHET MEASURES 248 1. MISE EN
SCENE: A BASIC QUESTION 248 2. A PREVIEW 249 3. PROJECTIVE BOUNDEDNESS
253 4. EVERY N * F 2 IS PROJECTIVELY BOUNDED 257 5. THERE EXIST
PROJECTIVELY UNBOUNDED ^-MEASURES 258 6. PROJECTIVE BOUNDEDNESS IN
TOPOLOGICAL SETTINGS 260 7. PROJECTIVE BOUNDEDNESS IN TOPOLOGICAL-GROUP
SETTINGS .V, 264 X CONTENTS 8. EXAMPLES 269 EXERCISES 272 HINTS FOR
EXERCISES IN CHAPTER IX : ... 276 X BROWNIAN MOTION AND THE WIENER
PROCESS 279 1. MISE EN SCENE: A HISTORICAL BACKDROP AND HEURISTICS 279
2. A MATHEMATICAL MODEL FOR BROWNIAN MOTION 285 3. THE WIENER INTEGRAL
288 4. SUB-GAUSSIAN SYSTEMS 295 5. RANDOM SERIES 300 6. VARIATIONS OF
THE WIENER F 2 -MEASURE 307 7. A MULTIPLE WIENER INTEGRAL 311 8. THE
BEGINNING OF ADAPTIVE STOCHASTIC INTEGRATION 316 9. SUB-A-SYSTEMS 320
10. MEASUREMENTS OF STOCHASTIC COMPLEXITY 322 11. THE NTH WIENER CHAOS
PROCESS AND ITS ASSOCIATED F-MEASURE 325 12. MISE EN SCENE (§1
CONTINUED): FURTHER APPROXIMATIONS OF BROWNIAN MOTION 329 13. RANDOM
WALKS AND DECISION MAKING N MACHINES 331 14. A-CHAOS: A DEFINITION, A
LIMIT THEOREM, AND SOME EXAMPLES 335 EXERCISES 339 HINTS FOR EXERCISES
IN CHAPTER X 344 XI INTEGRATORS 348 1. MISE EN SCENE: A GENERAL VIEW 348
2. INTEGRATORS AND INTEGRALS 350 3. EXAMPLES 357 4. MORE EXAMPLES:
A-CHAOS, A(G)-PROCESSES, P-STABLE MOTIONS 363 5. TWO QUESTIONS - A
PREVIEW 379 6. AN APPLICATION OF THE GROTHENDIECK FACTORIZATION THEOREM
385 7. INTEGRATORS INDEXED BY N-DIMENSIONAL SETS 388 8. EXAMPLES: RANDOM
CONSTRUCTIONS 396 9. INDEPENDENT PRODUCTS OF INTEGRATORS 397 10.
PRODUCTS.OF A WIENER PROCESS 402 11. RANDOM INTEGRANDS IN ONE PARAMETER
409 CONTENTS XI EXERCISES 419 HINTS FOR EXERCISES IN CHAPTER XI 424 XII
A 3/2-DIMENSIONAL CARTESIAN PRODUCT 427 1. MISE EN SCENE: TWO BASIC
QUESTIONS 427 2. A LITTLEWOOD INEQUALITY IN DIMENSION 3/2 428 3. A
KHINTCHIN INEQUALITY IN DIMENSION 3/2 434 4. TENSOR PRODUCTS IN
DIMENSION 3/2 440 5. FRECHET MEASURES IN DIMENSION 3/2 447 6.
PRODUCT -F-MEASURES AND PROJECTIVE BOUNDEDNESS IN DIMENSION 3/2 451
EXERCISES 453 HINTS FOR EXERCISES IN CHAPTER XII 455 XIII FRACTIONAL
CARTESIAN PRODUCTS AND COMBINATORIAL DIMENSION 456 1. MISE EN SCENE:
FRACTIONAL PRODUCTS 456 2. A LITTLEWOOD INEQUALITY IN FRACTIONAL
DIMENSION 458 3. A KHINTCHIN INEQUALITY IN FRACTIONAL DIMENSION 470
4. COMBINATORIAL DIMENSION 475 5. FRACTIONAL CARTESIAN PRODUCTS ARE
G-PRODUCTS 478 6. RANDOM CONSTRUCTIONS 483 7. A RELATION BETWEEN THE
DIM-SCALE AND THE CR-SCALE 488 8. A RELATION BETWEEN THE DIM-SCALE AND
THE 5-SCALE 495 EXERCISES 500 HINTS FOR EXERCISES IN CHAPTER XIII 501
XIV THE LAST CHAPTER: LEADS AND LOOSE ENDS 502 1. MISE EN SCENE: THE
LAST CHAPTER 502 2. FRECHET MEASURES IN FRACTIONAL DIMENSIONS 503 3.
COMBINATORIAL DIMENSION IN TOPOLOGICAL ~ AND MEASURABLE SETTINGS 516 4.
HARMONIC ANALYSIS 518 5. RANDOM WALKS 521 6. A-CHAOS 525 7. INTEGRATORS
IN FRACTIONAL DIMENSIONS 528 EXERCISES 531 HINTS FOR EXERCISES IN
CHAPTER XIV 533 REFERENCES 534 INDEX 547
|
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| dewey-search | 515.2433 |
| dewey-sort | 3515.2433 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
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| id | DE-604.BV013859195 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:53:17Z |
| institution | BVB |
| isbn | 0521650844 |
| language | English |
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| physical | XIX, 556 S. |
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| publisher | Cambridge Univ. Press |
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| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Blei, Ron Verfasser aut Analysis in integer and fractional dimensions Ron Blei 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2001 XIX, 556 S. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 71 MA0000485 Analisi armonica sbt Analisi funzionale sbt Dimension - Harmonische Analyse - Funktionalanalysis - Wahrscheinlichkeitstheorie Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Ungleichung (DE-588)4139098-2 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s Funktionalanalysis (DE-588)4018916-8 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Ungleichung (DE-588)4139098-2 s DE-604 Cambridge studies in advanced mathematics 71 (DE-604)BV000003678 71 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009478748&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Blei, Ron Analysis in integer and fractional dimensions Cambridge studies in advanced mathematics Analisi armonica sbt Analisi funzionale sbt Dimension - Harmonische Analyse - Funktionalanalysis - Wahrscheinlichkeitstheorie Funktionalanalysis (DE-588)4018916-8 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Harmonische Analyse (DE-588)4023453-8 gnd Ungleichung (DE-588)4139098-2 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4079013-7 (DE-588)4023453-8 (DE-588)4139098-2 |
| title | Analysis in integer and fractional dimensions |
| title_auth | Analysis in integer and fractional dimensions |
| title_exact_search | Analysis in integer and fractional dimensions |
| title_full | Analysis in integer and fractional dimensions Ron Blei |
| title_fullStr | Analysis in integer and fractional dimensions Ron Blei |
| title_full_unstemmed | Analysis in integer and fractional dimensions Ron Blei |
| title_short | Analysis in integer and fractional dimensions |
| title_sort | analysis in integer and fractional dimensions |
| topic | Analisi armonica sbt Analisi funzionale sbt Dimension - Harmonische Analyse - Funktionalanalysis - Wahrscheinlichkeitstheorie Funktionalanalysis (DE-588)4018916-8 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Harmonische Analyse (DE-588)4023453-8 gnd Ungleichung (DE-588)4139098-2 gnd |
| topic_facet | Analisi armonica Analisi funzionale Dimension - Harmonische Analyse - Funktionalanalysis - Wahrscheinlichkeitstheorie Funktionalanalysis Wahrscheinlichkeitstheorie Harmonische Analyse Ungleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009478748&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT bleiron analysisinintegerandfractionaldimensions |