Functional analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1971
|
| Edition: | 3. ed. |
| Series: | Grundlehren der mathematischen Wissenschaften
123 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 475 S. |
| ISBN: | 3540055061 0387055061 |
Staff View
MARC
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| 245 | 1 | 0 | |a Functional analysis |c by Kōsaku Yoshida |
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Record in the Search Index
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|---|---|
| adam_text | KOSAKU YOSIDA FUNCTIONAL ANALYSIS THIRD EDITION SPRINGER-VERLAG BERLIN
HEIDELBERG NEW YORK 1971 CONTENTS 0. PRELIMINARIES .1 1. SET THEORY 1 2.
TOPOLOGICAL SPACES 3 3. MEASURE SPACES 15 4. LINEAR SPACES 20 1.
SEMI-NORMS 23 1. SEMI-NORMS AND LOCALLY CONVEX LINEAR TOPOLOGICAL SPACES
. 23 2. NORMS AND QUASI-NORMS 30 3. EXAMPLES OF NORMED LINEAR SPACES 32
4. EXAMPLES OF QUASI-NORMED LINEAR SPACES 38 5. PRE-HILBERT SPACES 39 6.
CONTINUITY OF LINEAR OPERATORS 42 7. BOUNDED SETS AND BORNOLOGIC SPACES
44 8. GENERALIZED FUNCTIONS AND GENERALIZED DERIVATIVES . . . . 46 9.
J5-SPACES AND F-SPACES 52 10. THE COMPLETION 56 11. FACTOR SPACES OF A
B-SPACE 59 12. THE PARTITION OF UNITY 60 13. GENERALIZED FUNCTIONS WITH
COMPACT SUPPORT 62 14. THE DIRECT PRODUCT OF GENERALIZED FUNCTIONS 65
II. APPLICATIONS OF THE BAIRE-HAUSDORFF THEOREM 68 1. THE UNIFORM
BOUNDEDNESS THEOREM AND THE RESONANCE THEOREM 68 2. THE VITALI-HAHN-SAKS
THEOREM 70 3. THE TERMWISE DIFFERENTIABILITY OF A SEQUENCE OF
GENERALIZED FUNCTIONS 72 4. THE PRINCIPLE OF THE CONDENSATION OF
SINGULARITIES . . . . 72 5. THE OPEN MAPPING THEOREM 75 6. THE CLOSED
GRAPH THEOREM 77 7. AN APPLICATION OF THE CLOSED GRAPH THEOREM
(HORMANDER S THEOREM) 80 III. THE ORTHOGONAL PROJECTION AND F. RIESZ
REPRESENTATION THEO- REM 81 1. THE ORTHOGONAL PROJECTION 81 2. NEARLY
ORTHOGONAL ELEMENTS 84 VIII CONTENTS 3. THE ASCOLI-ARZELA THEOREM 85 4.
THE ORTHOGONAL BASE. BESSEL S INEQUALITY AND PARSEVAL S RELATION 86 5.
E. SCHMIDT S ORTHOGONALIZATION 88 6. F. RIESZ REPRESENTATION THEOREM 90
7. THE LAX-MILGRAM THEOREM 92 8. A PROOF OF THE LEBESGUE-NIKODYM THEOREM
93 9. THE ARONSZAJN-BERGMAN REPRODUCING KERNEL 95 10. THE NEGATIVE NORM
OF P. LAX 98 11. LOCAL STRUCTURES OF GENERALIZED FUNCTIONS 100 IV. THE
HAHN-BANACH THEOREMS 102 1. THE HAHN-BANACH EXTENSION THEOREM IN REAL
LINEAR SPACES 102 2. THE GENERALIZED LIMIT 103 3. LOCALLY CONVEX,
COMPLETE LINEAR TOPOLOGICAL SPACES . . . 104 4. THE HAHN-BANACH
EXTENSION THEOREM IN COMPLEX LINEAR SPACES 105 5. THE HAHN-BANACH
EXTENSION THEOREM IN NORMED LINEAR SPACES 106 6. THE EXISTENCE OF
NON-TRIVIAL CONTINUOUS LINEAR FUNCTIONALS 107 7. TOPOLOGIES OF LINEAR
MAPS . . .* 110 8. THE EMBEDDING OF X IN ITS BIDUAL SPACE X 112 9.
EXAMPLES OF DUAL SPACES 114 V. STRONG CONVERGENCE AND WEAK CONVERGENCE
119 1. THE WEAK CONVERGENCE AND THE WEAK* CONVERGENCE . . .120 2. THE
LOCAL SEQUENTIAL WEAK COMPACTNESS OF REFLEXIVE B- SPACES. THE UNIFORM
CONVEXITY 126 3. DUNFORD S THEOREM AND THE GELFAND-MAZUR THEOREM . . .
128 4. THE WEAK AND STRONG MEASURABILITY. PETTIS THEOREM . . . 130 5.
BOCHNER S INTEGRAL 132 APPENDIX TO CHAPTER V. WEAK TOPOLOGIES AND
DUALITY IN LOCALLY CONVEX LINEAR TOPOLOGICAL SPACES 136 1. POLAR SETS
136 2. BARREL SPACES 138 3. SEMI-REFLEXIVITY AND REFLEXIVITY 139 4. THE
EBERLEIN-SHMULYAN THEOREM 141 VI. FOURIER TRANSFORM AND DIFFERENTIAL
EQUATIONS 145 1. THE FOURIER TRANSFORM OF RAPIDLY DECREASING FUNCTIONS .
146 2. THE FOURIER TRANSFORM OF TEMPERED DISTRIBUTIONS 149 3.
CONVOLUTIONS 156 4. THE PALEY-WIENER THEOREMS. THE ONE-SIDED LAPLACE
TRANS- FORM 161 5. TITCHMARSH S THEOREM . 166 6. MIKUSINSKI S
OPERATIONAL CALCULUS 169 7. SOBOLEV S LEMMA 173 CONTENTS IX 8. GARDING S
INEQUALITY 175 9. FRIEDRICHS THEOREM 177 10. THE MALGRANGE-EHRENPREIS
THEOREM 182 11. DIFFERENTIAL OPERATORS WITH UNIFORM STRENGTH 188 12. THE
HYPOELLIPTICITY (HORMANDER S THEOREM) 189 VII. DUAL OPERATORS 193 3.
DUAL OPERATORS 193 2. ADJOINT OPERATORS 195 3. SYMMETRIC OPERATORS AND
SELF-ADJOINT OPERATORS 197 4. UNITARY OPERATORS. THE CAYLEY TRANSFORM
202 5. THE CLOSED RANGE THEOREM 205 VIII. RESOLVENT AND SPECTRUM 209 1.
THE RESOLVENT AND SPECTRUM 209 2. THE RESOLVENT EQUATION AND SPECTRAL
RADIUS 211 3. THE MEAN ERGODIC THEOREM 213 4. ERGODIC THEOREMS OF THE
HILLE TYPE CONCERNING PSEUDO- RESOLVENTS 215 5. THE MEAN VALUE OF AN
ALMOST PERIODIC FUNCTION 218 6. THE RESOLVENT OF A DUAL OPERATOR 224 7.
DUNFORD S INTEGRAL 225 8. THE ISOLATED SINGULARITIES OF A RESOLVENT 228
IX. ANALYTICAL THEORY OF SEMI-GROUPS 231 1. THE SEMI-GROUP OF CLASS (C O
) 232 2. THE EQUI-CONTINUOUS SEMI-GROUP OF CLASS (C O ) IN LOCALLY
CONVEX SPACES. EXAMPLES OF SEMI-GROUPS 234 3. THE INFINITESIMAL
GENERATOR OF AN EQUI-CONTINUOUS SEMI- GROUP OF CLASS (C O ) 237 4. THE
RESOLVENT OF THE INFINITESIMAL GENERATOR A 240 5. EXAMPLES OF
INFINITESIMAL GENERATORS 242 6. THE EXPONENTIAL OF A CONTINUOUS LINEAR
OPERATOR WHOSE POWERS ARE EQUI-CONTINUOUS 244 7. THE REPRESENTATION AND
THE CHARACTERIZATION OF EQUI-CON- TINUOUS SEMI-GROUPS OF CLASS (C O ) IN
TERMS OF THE CORRE- SPONDING INFINITESIMAL GENERATORS 246 8. CONTRACTION
SEMI-GROUPS AND DISSIPATIVE OPERATORS . . . . 250 9. EQUI-CONTINUOUS
GROUPS OF CLASS (C O ). STONE S THEOREM . . 251 10. HOLOMORPHIC
SEMI-GROUPS 254 11. FRACTIONAL POWERS OF CLOSED OPERATORS 259 12. THE
CONVERGENCE OF SEMI-GROUPS. TH6 TROTTER-KATO THEOREM 269 13. DUAL
SEMI-GROUPS. PHILLIPS THEOREM 272 X. COMPACT OPERATORS 274 1. COMPACT
SETS IN B-SPACES 274 2. COMPACT OPERATORS AND NUCLEAR OPERATORS 277 X
CONTENTS 3. THE RELLICH-GARDING THEOREM 281 4. SCHAUDER S THEOREM 282 5.
THE RIESZ-SCHAUDER THEORY 283 6. DIRICHLET S PROBLEM 286 APPENDIX TO
CHAPTER X. THE NUCLEAR SPACE OF A. GROTHENDIECK 289 XI. NORMED RINGS AND
SPECTRAL REPRESENTATION 294 1. MAXIMAL IDEALS OF A NORMED RING 295 2.
THE RADICAL. THE SEMI-SIMPLICITY 298 3. THE SPECTRAL RESOLUTION OF
BOUNDED NORMAL OPERATORS . . 302 4. THE SPECTRAL RESOLUTION OF A UNITARY
OPERATOR 306 5. THE RESOLUTION OF THE IDENTITY 309 6. THE SPECTRAL
RESOLUTION OF A SELF-ADJOINT OPERATOR . . . . 313 7. REAL OPERATORS AND
SEMI-BOUNDED OPERATORS. FRIEDRICHS THEOREM 316 8. THE SPECTRUM OF A
SELF-ADJOINT OPERATOR. RAYLEIGH S PRIN- CIPLE AND THE KRYLOV-WEINSTEIN
THEOREM. THE MULTIPLICITY OF THE SPECTRUM 319 9. THE GENERAL EXPANSION
THEOREM. A CONDITION FOR THE ABSENCE OF THE CONTINUOUS SPECTRUM 323 10.
THE PETER-WEYL-NEUMANN THEOREM 326 11. TANNAKA S DUALITY THEOREM FOR
NON-COMMUTATIVE COMPACT GROUPS 332 12. FUNCTIONS OF A SELF-ADJOINT
OPERATOR 338 13. STONE S THEOREM AND BOCHNER S THEOREM 345 14. A
CANONICAL FORM OF A SELF-AD JOINT OPERATOR WITH SIMPLE SPECTRUM 347 15.
THE DEFECT INDICES OF A SYMMETRIC OPERATOR. THE GENERALIZED RESOLUTION
OF THE IDENTITY 349 16. THE GROUP-RING L 1 AND WIENER S TAUBERIAN
THEOREM . . . 354 XII. OTHER REPRESENTATION THEOREMS IN LINEAR SPACES
362 1. EXTREMAL POINTS. THE KREIN-MILMAN THEOREM 362 2. VECTOR LATTICES
364 3. 5-LATTICES AND F-LATTICES 369 4. A CONVERGENCE THEOREM OF BANACH
370 5. THE REPRESENTATION OF A VECTOR LATTICE AS POINT FUNCTIONS 372 6.
THE REPRESENTATION OF A VECTOR LATTICE AS SET FUNCTIONS . 375 XIII.
ERGODIC THEORY AND DIFFUSION THEORY 379 1. THE MARKOV PROCESS WITH AN
INVARIANT MEASURE 379 2. AN INDIVIDUAL ERGODIC THEOREM AND ITS
APPLICATIONS . . . 383 3. THE ERGODIC HYPOTHESIS AND THE //-THEOREM 389
4. THE ERGODIC DECOMPOSITION OF A MARKOV PROCESS WITH A LOCALLY COMPACT
PHASE SPACE 393 5. THE BROWNIAN MOTION ON A HOMOGENEOUS RIEMANNIAN SPACE
398 6. THE GENERALIZED LAPLACIAN OF W. FELLER 403 7. AN EXTENSION OF THE
DIFFUSION OPERATOR 408 8. MARKOV PROCESSES AND POTENTIALS 410 9.
ABSTRACT POTENTIAL OPERATORS AND SEMI-GROUPS 411 CONTENTS XI XIV. THE
INTEGRATION OF THE EQUATION OF EVOLUTION 418 1. INTEGRATION OF DIFFUSION
EQUATIONS IN L 2 (R M ) 419 2. INTEGRATION OF DIFFUSION EQUATIONS IN A
COMPACT RIE- MANNIAN SPACE 425 3. INTEGRATION OF WAVE EQUATIONS IN A
EUCLIDEAN SPACE R M 427 4. INTEGRATION OF TEMPORALLY INHOMOGENEOUS
EQUATIONS OF EVOLUTION IN A B-SPACE 430 5. THE METHOD OF TANABE AND
SOBOLEVSKI 438 BIBLIOGRAPHY 447 INDEX 463
|
| any_adam_object | 1 |
| author | Yoshida, Kōsaku 1909-1990 |
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| dewey-search | 515/.7 |
| dewey-sort | 3515 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:07:59Z |
| institution | BVB |
| isbn | 3540055061 0387055061 |
| language | English |
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| physical | XI, 475 S. |
| publishDate | 1971 |
| publishDateSearch | 1971 |
| publishDateSort | 1971 |
| publisher | Springer |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Yoshida, Kōsaku 1909-1990 Verfasser (DE-588)119082519 aut Functional analysis by Kōsaku Yoshida 3. ed. Berlin u.a. Springer 1971 XI, 475 S. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 123 Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Funktionalanalysis (DE-588)4018916-8 s DE-604 Grundlehren der mathematischen Wissenschaften 123 (DE-604)BV000000395 123 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002540529&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yoshida, Kōsaku 1909-1990 Functional analysis Grundlehren der mathematischen Wissenschaften Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4123623-3 |
| title | Functional analysis |
| title_auth | Functional analysis |
| title_exact_search | Functional analysis |
| title_full | Functional analysis by Kōsaku Yoshida |
| title_fullStr | Functional analysis by Kōsaku Yoshida |
| title_full_unstemmed | Functional analysis by Kōsaku Yoshida |
| title_short | Functional analysis |
| title_sort | functional analysis |
| topic | Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Functional analysis Funktionalanalysis Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002540529&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT yoshidakosaku functionalanalysis |