Integral representation theory: applications to convexity, Banach spaces and potential theory
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
de Gruyter
2010
|
| Schriftenreihe: | De Gruyter studies in mathematics
35 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XVI, 715 S. |
| ISBN: | 9783110203202 |
Internformat
MARC
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| 245 | 1 | 0 | |a Integral representation theory |b applications to convexity, Banach spaces and potential theory |c Jaroslav Lukeš ... |
| 264 | 1 | |a Berlin [u.a.] |b de Gruyter |c 2010 | |
| 300 | |a XVI, 715 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a De Gruyter studies in mathematics |v 35 | |
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| 650 | 4 | |a Convex domains | |
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| 650 | 4 | |a Integral representations | |
| 650 | 4 | |a Potential theory (Mathematics) | |
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Datensatz im Suchindex
| _version_ | 1805093170672828416 |
|---|---|
| adam_text |
4.2 BARYCENTRIC THEOREM AND STRONGLY AFFINE FUNCTIONS 113 CONTENTS
INTRODUCTION V 1 PROLOGUE 1 1.1 THE KOROVKIN THEOREM 1 1.2 NOTES AND
COMMENTS 3 2 COMPACT CONVEX SETS 4 2.1 GEOMETRY OF CONVEX SETS 5 2.1 .A
FINITE-DIMENSIONAL CASE 5 2.1.B THE KREIN-MILMAN THEOREM 9 2.1.C EXPOSED
POINTS 21 2.2 INTERLUDE: ON THE SPACE M{K) 22 2.3 STRUCTURES IN CONVEX
SETS 26 2.3.A EXTREMAL SETS AND FACES 26 2.3.B MEASURE CONVEX SETS 30
2.3.C MEASURE EXTREMAL SETS 36 2.4 EXERCISES 40 2.5 NOTES AND COMMENTS
49 3 CHOQUET THEORY OF FUNCTION SPACES 52 3.1 FUNCTION SPACES 53 3.2
MORE ABOUT KOROVKIN THEOREMS 64 3.3 ON THE W-BARYCENTER MAPPING 66 3.4
THE CHOQUET REPRESENTATION THEOREM 67 3.5 IN-BETWEEN THEOREMS 70 3.6
MAXIMAL MEASURES 73 3.7 BOUNDARIES AND THE SIMONS LEMMA 78 3.8 THE
BISHOP-DE LEEUW THEOREM 81 3.9 MINIMUM PRINCIPLES 84 3.10 ORDERINGS AND
DILATIONS 86 3.11 EXERCISES 95 3.12 NOTES AND COMMENTS 105 4 AFFINE
FBNCTIONS ON COMPACT CONVEX SETS 107 4.1 AFFINE FUNCTIONS AND THE
BARYCENTRIC FORMULA 107 BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/997086351 DIGITALISIERT DURCH . 4.3 STATE SPACE AND
REPRESENTATION OF AFFINE FUNCTIONS 120 4.4 AFFINE BAIRE-ONE FUNCTIONS ON
DUAL UNIT BALLS 127 4.5 EXERCISES 129 4.6 NOTES AND COMMENTS 133 PERFECT
CLASSES OF FUNCTIONS AND REPRESENTATION OF AFFINE FUNCTIONS 135 5.1
GENERATION OF SETS AND FUNCTIONS 136 5.2 BAIRE AND BOREL SETS 142 5.3
BAIRE AND BOREL MAPPINGS 146 5.4 PERFECT CLASSES OF FUNCTIONS 149 5.5
AFFINELY PERFECT CLASSES OF FUNCTIONS 150 5.6 REPRESENTATION OF %-AFFINE
FUNCTIONS 154 5.7 EXERCISES 159 5.8 NOTES AND COMMENTS 166 SIMPLICIAL
FUNCTION SPACES 168 6.1 BASIC PROPERTIES OF SIMPLICIAL SPACES 169 6.2
CHARACTERIZATIONS OF SIMPLICIAL SPACES 176 6.3 SIMPLICIAL SPACES AS
L'-PREDUALS 178 6.4 THE WEAK DIRICHLET PROBLEM AND *4 C (%)-EXPOSED
POINTS 180 6.5 THE DIRICHLET PROBLEM FOR A SINGLE FUNCTION 182 6.6
SPECIAL CLASSES OF SIMPLICIAL SPACES 185 6.6.A BAUER SIMPLICIAL SPACES
185 6.6.B MARKOV SIMPLICIAL SPACES 188 6.6.C SIMPLICIAL SPACES WITH
LINDELOEF BOUNDARIES 190 6.6.D SIMPLICIAL SPACES WITH BOUNDARIES OF TYPE
F A 192 6.7 THE DAUGAVET PROPERTY OF SIMPLICIAL SPACES 196 6.8 CHOQUET
SIMPLICES 198 6.8.A SIMPLICIAL FUNCTION SPACES AND THE CLASSICAL
DEFINITION OF CHOQUET SIMPLICES 198 6.8.B PRIME FUNCTION SPACES AND
PRIME COMPACT CONVEX SETS . . 7.5 ORDERED COMPACT CONVEX SETS AND
SIMPLICIAL MEASURES 232 7.6 EXERCISES 240 7.7 NOTES AND COMMENTS 243 8
CHOQUET-LIKE SETS 244 8.1 SPLIT AND PARALLEL FACES 244 8.2 H -EXTREMAL
AND %-CONVEX SETS 246 8.3 CHOQUET SETS, M-SETS AND P-SETS 250 8.4
%-EXPOSED SETS 257 8.5 WEAK TOPOLOGY ON BOUNDARY MEASURES 259 8.6
CHARACTERIZATIONS OF SIMPLICIALITY BY CHOQUET SETS 262 8.7 EXERCISES 268
8.8 NOTES AND COMMENTS 273 9 TOPOLOGIES ON BOUNDARIES 274 9.1 TOPOLOGIES
GENERATED BY EXTREMAL SETS 274 9.2 INDUCED MEASURES ON CHOQUET
BOUNDARIES 278 9.3 FUNCTIONS CONTINUOUS IN A EN AND CR MAX TOPOLOGIES
284 9.4 STRONGLY UNIVERSALLY MEASURABLE FUNCTIONS 288 9.5 FACIAL
TOPOLOGY GENERATED BY M-SETS 296 9.6 EXERCISES 303 9.7 NOTES AND
COMMENTS 308 10 DEEPER RESULTS ON FUNCTION SPACES AND COMPACT CONVEX
SETS 310 10.1 BOUNDARIES 311 10.1.A SHILOV BOUNDARY 311 10.1.B
BOUNDARIES IN BANACH SPACES 314 10.2 ISOMETRIES OF SPACES OF AFFINE
CONTINUOUS FUNCTIONS 320 10.3 BAIRE MEASURABILITY AND BOUNDEDNESS OF
AFFINE FUNCTIONS 323 10.3.A THE CANTOR SET AND ITS PROPERTIES 323 10.3.B
AUTOMATIC BOUNDEDNESS OF AFFINE AND CONVEX FUNCTIONS . . . . 328 10.4
EMBEDDINGOR 1 335 10.5 METRIZABILITY OF COMPACT CONVEX SETS 338 10.
10.10 EXERCISES 378 10.11 NOTES AND COMMENTS 384 11 CONTINUOUS AND
MEASURABLE SELECTORS 389 11.1 THE LAZAR SELECTION THEOREM 389 11.2
APPLICATIONS OF THE LAZAR SELECTION THEOREM 394 11.3 THE WEAK DIRICHLET
PROBLEM FOR BAIRE FUNCTIONS 398 11.4 POINTWISE APPROXIMATION OF MAXIMAL
MEASURES 400 11.5 MEASURABLE SELECTORS 402 11.5.A MULTIVALUED MAPPINGS
402 11.5.B SELECTION THEOREM 406 11.5.C APPLICATIONS OF THE SELECTION
THEOREM 409 11.6 EXERCISES 412 11.7 NOTES AND COMMENTS 416 12
CONSTRUCTIONS OF FUNCTION SPACES 419 12.1 PRODUCTS OF FUNCTION SPACES
420 12.1.A DEFINITIONS AND BASIC PROPERTIES 420 12.1.B MAXIMAL MEASURES
AND EXTREMAL SETS 424 12.1 .C PARTITIONS OF UNITY AND APPROXIMATION IN
PRODUCTS OF FUNCTION SPACES 428 12.1.D PRODUCTS OF SIMPLICIAL SPACES 436
12.2 INVERSE LIMITS OF FUNCTION SPACES 440 12.2.A ADMISSIBLE MAPPINGS
440 12.2.B CONSTRUCTION OF INVERSE LIMITS 442 12.2.C INVERSE LIMITS OF
SIMPLICIAL FUNCTION SPACES 445 12.2.D STRUCTURE OF SIMPLICES 447 12.3
SEVERAL EXAMPLES 455 12.3.A THE POULSEN SIMPLEX 455 12.3.B A BIG
SIMPLICIAL SPACE 465 12.3.C FUNCTIONS OF AFFINE CLASSES AND TALAGRAND'S
EXAMPLE 470 12.4 EXERCISES 477 12.5 NOTES AND COMMENTS 486 13 FUNCTION
SPACES IN POTENTIAL THEORY AND THE DIRICHLET PROBLEM 489 13.1 BALAYAGE
AND THE DIRICHLET PROBLEM . 491 13.1. 13.3.B FUNCTION SPACES AND CONES
IN PARABOLIC POTENTIAL THEORY AND HARMONIC SPACES 510 13.3.C CONTINUITY
PROPERTIESOF H(C/)-CONCAVE FUNCTIONS 513 13.3.D SEPARATION BY FUNCTIONS
FROM H(/) 515 13.4 DIRICHLET PROBLEM: SOLUTION METHODS 517 13.4.A PWB
SOLUTION OF THE DIRICHLET PROBLEM 518 13.4.B CORNEA'S APPROACH TO THE
DIRICHLET PROBLEM 523 13.4.C THE WIENER SOLUTION 530 13.4.D FINE WIENER
SOLUTION 532 13.4.E PDE SOLUTIONS IN SOBOLEV SPACES 534 13.5 GENERALIZED
DIRICHLET PROBLEM AND UNIQUENESS QUESTIONS 537 13.5.A LATTICE APPROACH
538 13.5.B UNIQUENESS FOR THE LAPLACE EQUATION 540 13.5.C KELDYSH
THEOREMS IN PARABOLIC AND AXIOMATIC POTENTIAL THEORIES 542 13.6
EXERCISES 546 13.7 NOTES AND COMMENTS 555 14 APPLICATIONS 563 14.1
REPRESENTATION OF CONVEX FUNCTIONS 564 14.2 REPRESENTATION OF CONCAVE
FUNCTIONS 567 14.3 DOUBLY STOCHASTIC MATRICES 572 14.4 THE
RIESZ-HERGLOTZ THEOREM 573 14.5 TYPICALLY REAL HOLOMORPHIC FUNCTIONS 575
14.6 HOLOMORPHIC FUNCTIONS WITH POSITIVE REAL PART 580 14.7 COMPLETELY
MONOTONIC FUNCTIONS 586 14.8 POSITIVE DEFINITE FUNCTIONS ON DISCRETE
GROUPS 589 14.9 RANGE OF VECTOR MEASURES 593 14.10THESTONE-WEIERSTRASS
APPROXIMATION THEOREM 595 14.11 INVARIANT AND ERGODIC MEASURES 597 14.12
EXERCISES 603 14.13 NOTES AND COMMENTS 605 A APPENDIX 608 A.1 FUNCTIONAL
ANALYSIS 608 A.L. A.3 MEASURE THEORY 624 A.3.A MEASURE SPACES 624 A.3.B
RADON MEASURES ON LOCALLY COMPACT CR-COMPACT SPACES . . . . 626 A.3.C
IMAGES, PRODUCTS AND INVERSE LIMITS OF RADON MEASURES . . . . 632 A.3.D
KERNELS AND DISINTEGRATION OF MEASURES 636 A.4 DESCRIPTIVE SET THEORY
637 A.5 RESOLVABLE SETS AND BAIRE-ONE FUNCTIONS 640 A.6 THE LAPLACE
EQUATION 645 A.6.A WEAK SOLUTIONS OF THE LAPLACE EQUATION 647 A.7 THE
HEAT EQUATION 649 A.8 AXIOMATIC POTENTIAL THEORY 652 A.8.A BAUER'S
AXIOMATIC THEORY 653 A.8.B HYPERHARMONIC AND SUPERHARMONIC FUNCTIONS 654
A.8.C POTENTIALS 656 A.8.D SUPERHARMONIC FUNCTIONS AND GREEN POTENTIALS
657 A.8.E SUPERHARMONIC FUNCTIONS AND POTENTIALS FOR THE HEAT EQUATION .
660 A.8.F BALAYAGE 661 A.8.G THINNESS, BASE AND FINE TOPOLOGY 663 A.8.H
POLAR AND SEMIPOLAR SETS 665 BIBLIOGRAPHY 669 LIST OF SYMBOLS 695 INDEX
703 |
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| indexdate | 2024-07-20T10:23:14Z |
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| isbn | 9783110203202 |
| language | English |
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| spelling | Integral representation theory applications to convexity, Banach spaces and potential theory Jaroslav Lukeš ... Berlin [u.a.] de Gruyter 2010 XVI, 715 S. txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics 35 Banach spaces Convex domains Functional analysis Integral representations Potential theory (Mathematics) Banach-Raum (DE-588)4004402-6 gnd rswk-swf Choquet-Theorie (DE-588)4638875-8 gnd rswk-swf Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Konvexe Menge (DE-588)4165212-5 gnd rswk-swf Integraldarstellung (DE-588)4127585-8 gnd rswk-swf Integraldarstellung (DE-588)4127585-8 s Konvexe Menge (DE-588)4165212-5 s Banach-Raum (DE-588)4004402-6 s Potenzialtheorie (DE-588)4046939-6 s DE-604 Choquet-Theorie (DE-588)4638875-8 s Lukeš, Jaroslav 1940- Sonstige (DE-588)111006066 oth De Gruyter studies in mathematics 35 (DE-604)BV000005407 35 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3360094&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018677562&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Integral representation theory applications to convexity, Banach spaces and potential theory De Gruyter studies in mathematics Banach spaces Convex domains Functional analysis Integral representations Potential theory (Mathematics) Banach-Raum (DE-588)4004402-6 gnd Choquet-Theorie (DE-588)4638875-8 gnd Potenzialtheorie (DE-588)4046939-6 gnd Konvexe Menge (DE-588)4165212-5 gnd Integraldarstellung (DE-588)4127585-8 gnd |
| subject_GND | (DE-588)4004402-6 (DE-588)4638875-8 (DE-588)4046939-6 (DE-588)4165212-5 (DE-588)4127585-8 |
| title | Integral representation theory applications to convexity, Banach spaces and potential theory |
| title_auth | Integral representation theory applications to convexity, Banach spaces and potential theory |
| title_exact_search | Integral representation theory applications to convexity, Banach spaces and potential theory |
| title_full | Integral representation theory applications to convexity, Banach spaces and potential theory Jaroslav Lukeš ... |
| title_fullStr | Integral representation theory applications to convexity, Banach spaces and potential theory Jaroslav Lukeš ... |
| title_full_unstemmed | Integral representation theory applications to convexity, Banach spaces and potential theory Jaroslav Lukeš ... |
| title_short | Integral representation theory |
| title_sort | integral representation theory applications to convexity banach spaces and potential theory |
| title_sub | applications to convexity, Banach spaces and potential theory |
| topic | Banach spaces Convex domains Functional analysis Integral representations Potential theory (Mathematics) Banach-Raum (DE-588)4004402-6 gnd Choquet-Theorie (DE-588)4638875-8 gnd Potenzialtheorie (DE-588)4046939-6 gnd Konvexe Menge (DE-588)4165212-5 gnd Integraldarstellung (DE-588)4127585-8 gnd |
| topic_facet | Banach spaces Convex domains Functional analysis Integral representations Potential theory (Mathematics) Banach-Raum Choquet-Theorie Potenzialtheorie Konvexe Menge Integraldarstellung |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3360094&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018677562&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005407 |
| work_keys_str_mv | AT lukesjaroslav integralrepresentationtheoryapplicationstoconvexitybanachspacesandpotentialtheory |