Banach Hilbert spaces, vector measures and group representations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2002
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 606 S. graph. Darst. |
| ISBN: | 9812380388 |
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Record in the Search Index
| _version_ | 1804129619349078016 |
|---|---|
| adam_text | BANACH-HILBERT SPACES, VECTOR MEASURES AND GROUP REPRESENTATIONS TSOY-WO
MA UNIVERSITY OF WESTERN AUSTRALIA WORLD SCIENTIFIC NEW JERSEY LONDON *
SINGAPORE * HONG KONG CONTENTS PREFACE V INTRODUCTION 1 CHAPTER 1 METRIC
SPACES 1-1 STANDARD FINITE DIMENSIONAL VECTOR SPACES 11 1-2 CONVERGENT
SEQUENCES IN METRIC SPACES 13 1-3 CONTINUOUS MAPS 14 1-4 OPEN SETS 17
1-5 CLOSURES OF SETS 18 1-6 CHARACTERIZATION OF CONTINUITY 20 1-7
DUALITY OF CLOSURE-INTERIOR OPERATORS 22 1-8 PARTITION OF UNITY 24
CHAPTER 2 COMPLETE, COMPACT AND CONNECTED SETS 2-1 CAUCHY SEQUENCES 27
2-2 BOUNDED SETS 28 2-3 UPPER AND LOWER LIMITS 29 2-4 COMPLETE SETS 31
2-5 PRECOMPACT SETS 33 2-6 COMPACTNESS 36 2-7 CONTINUOUS MAPS ON COMPACT
SPACES 39 2-8 UNIFORM CONTINUITY 41 2-9 CONNECTED SETS 43 2-10.
COMPONENTS 46 CHAPTER 3 BANACH SPACES 3-1 UNIFORM CONVERGENCE 48 3-2
BOUNDED CONTINUOUS FUNCTIONS 49 3-3 SEQUENCE SPACES 52 3-4 CONTINUOUS
LINEAR MAPS 55 3-5 EXAMPLES OF CONTINUOUS LINEAR MAPS 59 3-6 FINITE
DIMENSIONAL NORMED SPACES 61 3-7 INFINITE DIMENSIONAL COMPACT SETS 64
3-8 APPROXIMATION IN FUNCTION SPACES 67 CHAPTER 4 SIMPLICIAL COMPLEXES
4-1 GEOMETRICALLY INDEPENDENT SETS 71 4-2 CONVEX SETS IN NORMED SPACES
75 4-3 SIMPLEXES 77 4-4 AFFINE MAPS 78 4-5 SIMPLICIAL COMPLEXES 80 4-6
SMALL SIMPLEXES 83 4-7 BARYCENTRIC SUBDIVISIONS 85 X CONTENTS 4-8
SIMPLICIAL APPROXIMATIONS 87 4-9 EXISTENCE OF SIMPLICIAL APPROXIMATIONS
89 4-10. A COMBINATORIAL LEMMA WITH APPLICATION 91 CHAPTER 5 TOPOLOGICAL
FIXED POINTS 5-1 ANTIPODAL MAPS 95 5-2 RETRACTS AND FIXED POINTS 98 5-3
FIXED POINTS OF COMPACT MAPS 101 5-4 COMPACT FIELDS AND THEIR HOMOTOPIES
102 5-5 EXTENSION PROPERTY 105 5-6 PROPERTIES OF COMPACT FIELDS IN
NORMED SPACES 109 CHAPTER 6 FOUNDATION OF FUNCTIONAL ANALYSIS 6-1
TRANSFINITE INDUCTION 114 6-2 HAHN-BANACH EXTENSION THEOREMS 116 6-3
EXTENSION OF CONTINUOUS LINEAR FORMS 118 6-4 CLOSED HYPERPLANES 120 6-5
SEPARATION BY HYPERPLANES 123 6-6 EXTREME POINTS 125 6-7 BAIRE S
PROPERTY 127 6-8 UNIFORM BOUNDEDNESS 128 6-9 OPEN MAP AND CLOSED GRAPH
THEOREMS 130 CHAPTER 7 NATURAL CONSTRUCTIONS 7-1 BIDUAL SPACES 134 7-2
QUOTIENT SPACES 136 7-3 DUALITY OF SUBSPACES AND QUOTIENTS 138 7-4
DIRECT SUMS 140 7-5 TRANSPOSES 144 7-6 REFLEXIVE SPACES 147 7-7 WEAK
CONVERGENCE 149 7-8 WEAK-STAR CONVERGENCE 152 CHAPTER 8 COMPLEX ANALYSIS
8-1 DERIVATIVES OF VECTOR MAPS 154 8-2 INTEGRALS OF REGULATED MAPS 155
8-3 FUNDAMENTAL THEOREMS OF CALCULUS 158 8-4 HOLOMORPHIC MAPS OF ONE
COMPLEX VARIABLE 161 8-5 SERIES EXPANSION 165 8-6 SPECTRUM 170 8-7
SPECTRAL RADIUS 174 8-8 HOLOMORPHIC MAPS OF AN OPERATOR 176 CONTENTS XI
CHAPTER 9 DIFFERENTIATION IN BANACH SPACES 9-1 DIFFERENTIABLE MAPS 182
9-2 MEAN-VALUE THEOREM 185 9-3 PARTIAL DERIVATIVES 188 9-4 FIXED POINTS
OF CONTRACTIONS 192 9-5 INVERSE AND IMPLICIT MAPPING THEOREMS 193 9-6
LOCAL PROPERTIES OF DIFFERENTIABLE MAPS 197 CHAPTER 10 POLYNOMIALS AND
HIGHER DERIVATIVES 10-1 MULTILINEAR MAPS ON BANACH SPACES 201 10-2
POLYNOMIALS ON BANACH SPACES 204 10-3 HIGHER DERIVATIVES 208 10-4
C -MAPS 211 10-5 TAYLOR S EXPANSION 215 10-6 HIGHER CHAIN FORMULA AND
HIGHER PRODUCT FORMULA 219 CHAPTER 11 ORDINARY DIFFERENTIAL EQUATIONS
11-1 LOCAL EXISTENCE AND UNIQUENESS 223 11-2 INTEGRAL CURVES 226 11-3
LINEAR EQUATIONS 228 11-4 EXPONENTIAL FUNCTIONS OF MATRICES 233 11-5
GLOBAL DEPENDENCE ON INITIAL CONDITIONS . 235 11-6 SOLUTIONS WITHOUT
UNIQUENESS 242 CHAPTER 12 COMPACT LINEAR OPERATORS 12-1 BASIC PROPERTIES
245 12-2 RIESZ-SCHAUDER THEORY 249 12-3 SPECTRUM OF A COMPACT OPERATOR
253 12-4 EXISTENCE OF INVARIANT SUBSPACES 254 12-5 FREDHOLM OPERATORS
256 CHAPTER 13 OPERATORS ON HILBERT SPACES 13-1 COMPLEX INNER PRODUCT
SPACES 261 13-2 ORTHOGONALITY IN INNER PRODUCT SPACES 263 13-3
ORTHONORMAL BASES OF HILBERT SPACES 265 13-4 ORTHOGONAL COMPLEMENTS 268
13-5 ADJOINTS 270 13-6 QUADRATIC FORMS 274 13-7 NORMAL OPERATORS 276
13-8 SELF-ADJOINT OPERATORS 278 13-9 PROJECTORS AND CLOSED VECTOR
SUBSPACES 280 13-10 PARTIAL ORDER OF OPERATORS 284 13-11 EIGENVALUES 288
XII CONTENTS CHAPTER 14 SPECTRAL PROPERTIES OF HILBERT SPACES 14-1
SPECTRUM OF AN OPERATOR 291 14-2 APPROXIMATE SPECTRUM 292 14-3 WEAK
CONVERGENCE 295 14-4 DIAGONAL OPERATORS 297 14-5 COMPACT OPERATORS 299
14-6 FUNCTIONAL CALCULUS OF SELF-ADJOINT OPERATORS 305 14-7 POLAR
DECOMPOSITION 310 CHAPTER 15 TENSOR PRODUCTS 15-1 ALGEBRAIC TENSOR
PRODUCTS OF VECTOR SPACES 313 15-2 TENSOR PRODUCTS OF LINEAR MAPS 315
15-3 INDEPENDENT SETS IN TENSOR PRODUCTS 317 15-4 MATRIX REPRESENTATIONS
319 15-5 PROJECTIVE NORMS ON TENSOR PRODUCTS 323 15-6 INDUCTIVE NORMS
327 15-7 TENSOR PRODUCT OF HILBERT SPACES 329 CHAPTER 16 COMPLEX VECTOR
LATTICES 16-1 ORDERED VECTOR SPACES 335 16-2 LATTICE STRUCTURE 336 16-3
DECOMPOSITION PROPERTY 339 16-4 EXTENSION OF POSITIVE LINEAR FORMS 341
16-5 ORDER BOUNDED LINEAR FORMS 343 CHAPTER 17 VECTOR MEASURES ON
SEMIRINGS 17-1 SEMIRINGS 346 17-2 CHARGES AND ASSOCIATED INTEGRALS 347
17-3 FINITE VARIATION 350 17-4 ABSOLUTELY CONVERGENT CHARGES 352 17-5
COUNTABLE ADDITIVITY ON RINGS 355 17-6 VECTOR MEASURES 358 17-7
LEBESGUE-STIELTJES MEASURES 360 CHAPTER 18 EXTENSIONS OF POSITIVE
MEASURES 18-1 UNIQUENESS OF EXTENSION 364 18-2 OUTER MEASURES 366 18-3
EXTENSION TO DECENT SETS 370 CHAPTER 19 MEASURABLE OBJECTS 19-1
MEASURABLE SETS 372 19-2 MEASURABLE FUNCTIONS 374 19-3 LIMITS OF
MEASURABLE FUNCTIONS 377 CONTENTS XIII 19-4 APPROXIMATIONS BY SIMPLE
FUNCTIONS .*- 378 19-5 MEASURABLE MAPS 380 19-6 MORE PROPERTIES 382
CHAPTER 20 INTEGRALS OF UPPER FUNCTIONS 20-1 UPPER FUNCTIONS 386 20-2
ALMOST EVERYWHERE 389 20-3 SEEDS OF THE THEORY 391 20-4 SIGMA FINITENESS
392 20-5 COMPARISON OF TWO POSITIVE MEASURES 394 CHAPTER 21 VECTOR
INTEGRALS 21-1 EXTENSION TO INTEGRABLE SETS 397 21-2 INTEGRALS OF VECTOR
MAPS 399 21-3 LP-SPACES FOR 1 P OO 402 21-4 MEAN CONVERGENCE 405
21-5 LOO-SPACES 408 21-6 CONVERGENCE IN MEASURE 410 21-7 ALMOST UNIFORM
CONVERGENCE 412 21-8 MORE THAN ONE MEASURE 416 21-9 INTEGRATION ON
SUBSPACES 417 CHAPTER 22 FINITE PRODUCTS OF MEASURES 22-1 PRODUCT
MEASURABLE SPACES 420 22-2 PRODUCT MEASURES 422 22-3 REPEATED INTEGRALS
424 CHAPTER 23 MEASURES ON FINITE DIMENSIONAL SPACES 23-1 DECENT SETS OF
IR 432 23-2 REGULARITY 433 23-3 TRANSLATION INVARIANCE 435 23-4
RELATION TO OUTER MEASURES 438 23-5 CHANGE VARIABLES IN H N 439 CHAPTER
24 INDEFINITE INTEGRALS 24-1 DERIVATIVES 445 24-2 ABSOLUTE CONTINUITY
448 24-3 POSITIVE AND NEGATIVE SETS 451 24-4 EXISTENCE OF DERIVATIVES
452 24-5 HAHN AND LEBESGUE DECOMPOSITIONS 456 24-6 DUALITY OF CLASSICAL
SPACES 458 24-7 SPACES WITH RADON-NIKODYM PROPERTY 466 XIV CONTENTS
CHAPTER 25 DIFFERENTIATION OF MEASURES 25-1 GEOMETRICAL EXPRESSION OF
RADON-NIKODYM DERIVATIVES 473 25-2 JUMPS OF INCREASING FUNCTIONS 477
25-3 FUNDAMENTAL THEOREMS OF REAL ANALYSIS 480 25-4 CANTOR SET AND
FUNCTION 484 CHAPTER 26 SPECTRAL MEASURES 26-1 CONSTRUCTION FROM
SELF-ADJOINT OPERATORS 487 26-2 EXTENSION OF SPECTRAL MEASURES 490 26-3
SPECTRAL INTEGRATION 495 26-4 NULL SETS OF SPECTRAL MEASURES 498 26-5
PRODUCT SPECTRAL MEASURES 501 26-6 SPECTRAL MEASURES OF NORMAL OPERATORS
503 CHAPTER 27 LOCALLY COMPACT SPACES 27-1 REGULAR MEASURES 509 27-2
CONSTRUCTION FROM POSITIVE LINEAR FORMS 512 27-3 REPRESENTATIONS OF
ORDER-BOUNDED LINEAR FORMS 515 CHAPTER 28 ALMOST PERIODIC FUNCTIONS ON
GROUPS 28-1 ALMOST PERIODICITY 518 28-2 MEAN VALUES 522 28-3
CONVOLUTIONS 527 28-4 EIGEN EXPANSION 532 CHAPTER 29 GROUP
REPRESENTATIONS 29-1 MATRIX REPRESENTATIONS 538 29-2 CHARACTERIZATION OF
PROJECTORS 543 29-3 FOURIER MATRICES 547 CHAPTER 30 SATURATED CLOSED
INVARIANT IDEALS 30-1 DUAL OBJECTS 553 30-2 CHARACTERS 555 30-3
SATURATED DUAL OBJECTS 560 30-4 SEPARATING POINTS 566 CHAPTER 31 MEAN
SPACES 31-1 REPRESENTATIONS OF PRODUCT GROUPS 571 31-2 MEANS ON GROUPS
575 31-3 ORDER STRUCTURE ON MEAN SPACES 578 31-4 IDENTIFICATION OF
FUNCTIONS AS MEANS 580 31-5 FOURIER MATRICES OF MEANS 583 REFERENCES 587
INDEX 599
|
| any_adam_object | 1 |
| author | Ma, Tsoy-Wo |
| author_facet | Ma, Tsoy-Wo |
| author_role | aut |
| author_sort | Ma, Tsoy-Wo |
| author_variant | t w m twm |
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| dewey-full | 515.7 |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7 |
| dewey-search | 515.7 |
| dewey-sort | 3515.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014855474 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:08:01Z |
| institution | BVB |
| isbn | 9812380388 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010047631 |
| oclc_num | 470152083 |
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| owner_facet | DE-824 DE-355 DE-BY-UBR DE-11 DE-188 |
| physical | XIV, 606 S. graph. Darst. |
| publishDate | 2002 |
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| publisher | World Scientific |
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| spelling | Ma, Tsoy-Wo Verfasser aut Banach Hilbert spaces, vector measures and group representations Tsoy-Wo Ma Banach-Hilbert spaces, vector measures and group representations New Jersey [u.a.] World Scientific 2002 XIV, 606 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Banach, Espaces de ram Espaces vectoriels ram Représentations de groupes ram Maßtheorie (DE-588)4074626-4 gnd rswk-swf Vektorwertiges Maß (DE-588)4187472-9 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Maßtheorie (DE-588)4074626-4 s Banach-Raum (DE-588)4004402-6 s DE-604 Vektorwertiges Maß (DE-588)4187472-9 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010047631&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ma, Tsoy-Wo Banach Hilbert spaces, vector measures and group representations Banach, Espaces de ram Espaces vectoriels ram Représentations de groupes ram Maßtheorie (DE-588)4074626-4 gnd Vektorwertiges Maß (DE-588)4187472-9 gnd Banach-Raum (DE-588)4004402-6 gnd |
| subject_GND | (DE-588)4074626-4 (DE-588)4187472-9 (DE-588)4004402-6 |
| title | Banach Hilbert spaces, vector measures and group representations |
| title_alt | Banach-Hilbert spaces, vector measures and group representations |
| title_auth | Banach Hilbert spaces, vector measures and group representations |
| title_exact_search | Banach Hilbert spaces, vector measures and group representations |
| title_full | Banach Hilbert spaces, vector measures and group representations Tsoy-Wo Ma |
| title_fullStr | Banach Hilbert spaces, vector measures and group representations Tsoy-Wo Ma |
| title_full_unstemmed | Banach Hilbert spaces, vector measures and group representations Tsoy-Wo Ma |
| title_short | Banach Hilbert spaces, vector measures and group representations |
| title_sort | banach hilbert spaces vector measures and group representations |
| topic | Banach, Espaces de ram Espaces vectoriels ram Représentations de groupes ram Maßtheorie (DE-588)4074626-4 gnd Vektorwertiges Maß (DE-588)4187472-9 gnd Banach-Raum (DE-588)4004402-6 gnd |
| topic_facet | Banach, Espaces de Espaces vectoriels Représentations de groupes Maßtheorie Vektorwertiges Maß Banach-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010047631&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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