Methods in classical and functional analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Reading, Mass. [u.a.]
Addison-Wesley
1972
|
| Schriftenreihe: | Addison-Wesley series in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 486 S. |
Internformat
MARC
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| 245 | 1 | 0 | |a Methods in classical and functional analysis |c Einar Hille |
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Datensatz im Suchindex
| _version_ | 1804117391711404032 |
|---|---|
| adam_text | CONTENTS
Chapter 1 Complex Euclidean Spaces
1.1 Euclidean three space 1
1.2 The space C 8
1.3 Linear transformations 13
1.4 Matrices 18
1.5 The resolvent 28
1.6 Invariantive and metric properties 36
1.7 Hermitian forms 42
Chapter 2 Linear Vector Spaces
2.1 Banach spaces 51
2.2 Linear transformations 56
2.3 Linear functionals . 60
2.4 Linear operator spaces 63
2.5 Inner product spaces 67
2.6 Banach algebras 80
Chapter 3 Some Special Linear Spaces
3.1 Sequence spaces 85
3.2 Continuous functions 96
3.3 Functions of bounded variation 107
Chapter 4 Lebesgue Spaces
4.1 The m dim Lebesgue measure 112
4.2 Lebesgue measurable functions 119
4.3 Lebesgue integration 123
4.4 Lebesgue spaces 136
4.5 Remarks on Fourier series 149
Chapter 5 Metric Spaces and Fixed Point Theorems
5.1 Metric spaces 159
5.2 Partial ordering 161
5.3 Contraction mappings 165
vii
viii CONTENTS
5.4 Contraction fixed point theorems 169
5.5 Contractive mappings 173
5.6 The Volterra fixed point theorem 176
5.7 Some applications 179
Chapter 6 Existence and Uniqueness Theorems
6.1 The implicit function theorem 189
6.2 The method of successive approximations 194
6.3 Majorants 199
6.4 Applications to ordinary differential equations 204
Chapter 7 Real Analysis in Linear Spaces
7.1 The principle of uniform boundedness 212
7.2 Topologies 217
7.3 Vector valued and operator valued functions 226
7.4 Abstract Riemann Stieltjes integrals 230
7.5 Bochner integrals 236
Chapter 8 Complex Analysis in Linear Spaces
8.1 Abstract holomorphic functions 249
8.2 Theorem of Vitali 258
8.3 Functions analytic in the sense of Frechet 264
8.4 Some properties of (F) analytic functions 271
Chapter 9 Banach Algebras
9.1 Review 276
9.2 Resolvents and dissolvents 281
9.3 Gelfand s representation theorem 290
9.4 (F) analytic functions and the operational calculus 296
Chapter 10 Linear Transformations
10.1 Boundedness 305
10.2 Closure 310
10.3 Linear functionals 317
10.4 Inverses and adjoints 322
10.5 Spectra and resolvents 325
Chapter 11 Inner Product Spaces
11.1 Review 331
11.2 Spectrum and the numerical range 335
11.3 Operational calculus 341
11.4 The spectral theorem 354
CONTENTS ix
Chapter 12 Functional Inequalities I. Functions of a Single Variable
12.1 Classification 362
12.2 Some determinative inequalities 364
12.3 Use of fixed point theorems 367
12.4 Some applications 373
12.5 Remarks on a class of multiplicative inequalities 376
Chapter 13 Functional Inequalities II. Functions on Product Spaces
13.1 Subadditive and suboperative functions 380
13.2 Semi modules and subadditive functions in Rm 386
13.3 Convex functions 400
13.4 Non Archimedean valuations 409
Chapter 14 Functional Equations
14.1 Cryptoanalysis 412
14.2 Cauchy s equations and generalizations 418
14.3 Uniqueness theorems 426
Chapter 15 Mean Values
15.1 The postulates : 437
15.2 Associated functional equations 439
15.3 Remarks on summability 449
15.4 Some geometric external problems 451
15.5 The transfinite A diameter 456
15.6 The Cebysev constants 459
15.7 Some examples 464
15.8 Potential theories 467
Index 475
|
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| author | Hille, Einar 1894-1980 |
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| author_facet | Hille, Einar 1894-1980 |
| author_role | aut |
| author_sort | Hille, Einar 1894-1980 |
| author_variant | e h eh |
| building | Verbundindex |
| bvnumber | BV003103898 |
| classification_rvk | SK 400 SK 600 |
| ctrlnum | (OCoLC)602764520 (DE-599)BVBBV003103898 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV003103898 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:53:40Z |
| institution | BVB |
| language | English |
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| physical | IX, 486 S. |
| publishDate | 1972 |
| publishDateSearch | 1972 |
| publishDateSort | 1972 |
| publisher | Addison-Wesley |
| record_format | marc |
| series2 | Addison-Wesley series in mathematics |
| spelling | Hille, Einar 1894-1980 Verfasser (DE-588)11909116X aut Methods in classical and functional analysis Einar Hille Reading, Mass. [u.a.] Addison-Wesley 1972 IX, 486 S. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in mathematics Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001946186&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hille, Einar 1894-1980 Methods in classical and functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 |
| title | Methods in classical and functional analysis |
| title_auth | Methods in classical and functional analysis |
| title_exact_search | Methods in classical and functional analysis |
| title_full | Methods in classical and functional analysis Einar Hille |
| title_fullStr | Methods in classical and functional analysis Einar Hille |
| title_full_unstemmed | Methods in classical and functional analysis Einar Hille |
| title_short | Methods in classical and functional analysis |
| title_sort | methods in classical and functional analysis |
| topic | Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Funktionalanalysis |
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