Advanced real analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
2005
|
| Schriftenreihe: | Cornerstones
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Erg. zu: Knapp, Anthony W.: Basic real analysis |
| Beschreibung: | XXII, 465 S. graph. Darst. |
| ISBN: | 0817643826 0817644075 9780817643829 0817644423 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804133600522665984 |
|---|---|
| adam_text | CONTENTS
List of Figures x
Preface xi
Dependence Among Chapters xiv
Guide for the Reader xv
Notation and Terminology xix
I. INTRODUCTION TO BOUNDARY VALUE PROBLEMS 1
1. Partial Differential Operators 1
2. Separation of Variables 3
3. Sturm Liouville Theory 19
4. Problems 31
II. COMPACT SELF ADJOINT OPERATORS 34
1. Compact Operators 34
2. Spectral Theorem for Compact Self Adjoint Operators 36
3. Hilbert Schmidt Theorem 41
4. Unitary Operators 45
5. Classes of Compact Operators 46
6. Problems 52
III. TOPICS IN EUCLIDEAN FOURIER ANALYSIS 54
1. Tempered Distributions 54
2. Weak Derivatives and Sobolev Spaces 60
3. Harmonic Functions 69
4. W Theory 80
5. Calderon Zygmund Theorem 83
6. Applications of the Calderon Zygmund Theorem 92
7. Multiple Fourier Series 96
8. Application to Traces of Integral Operators 97
9. Problems 99
vii
viii Contents
IV. TOPICS IN FUNCTIONAL ANALYSIS 105
1. Topological Vector Spaces 106
2. C°°(U), Distributions, and Support 112
3. Weak and Weak Star Topologies, Alaoglu s Theorem 116
4. Stone Representation Theorem 121
5. Linear Functionals and Convex Sets 125
6. Locally Convex Spaces 128
7. Topology on C~m(l/) 131
8. Krein Milman Theorem 140
9. Fixed Point Theorems 143
10. Gelfand Transform for Commutative C* Algebras 146
11. Spectral Theorem for Bounded Self Adjoint Operators 160
12. Problems 173
V. DISTRIBUTIONS 179
1. Continuity on Spaces of Smooth Functions 179
2. Elementary Operations on Distributions 187
3. Convolution of Distributions 189
4. Role of Fourier Transform 202
5. Fundamental Solution of Laplacian 206
6. Problems 207
VI. COMPACT AND LOCALLY COMPACT GROUPS 212
1. Topological Groups 213
2. Existence and Uniqueness of Haar Measure 220
3. Modular Function 230
4. Invariant Measures on Quotient Spaces 234
5. Convolution and Lp Spaces 237
6. Representations of Compact Groups 240
7. Peter Weyl Theorem 251
8. Fourier Analysis Using Compact Groups 256
9. Problems 264
VII. ASPECTS OF PARTIAL DIFFERENTIAL EQUATIONS 275
1. Introduction via Cauchy Data 275
2. Orientation 283
3. Local Solvability in the Constant Coefficient Case 292
4. Maximum Principle in the Elliptic Second Order Case 296
5. Parametrices for Elliptic Equations with Constant Coefficients 300
6. Method of Pseudodifferential Operators 305
7. Problems 317
Contents ix
VIII. ANALYSIS ON MANIFOLDS 321
1. Differential Calculus on Smooth Manifolds 322
2. Vector Fields and Integral Curves 331
3. Identification Spaces 334
4. Vector Bundles 338
5. Distributions and Differential Operators on Manifolds 348
6. More about Euclidean Pseudodifferential Operators 355
7. Pseudodifferential Operators on Manifolds 361
8. Further Developments 366
9. Problems 370
IX. FOUNDATIONS OF PROBABILITY 375
1. Measure Theoretic Foundations 375
2. Independent Random Variables 381
3. Kolmogorov Extension Theorem 386
4. Strong Law of Large Numbers 393
5. Problems 399
Hints for Solutions of Problems 403
Selected References 451
Index of Notation 455
Index 459
|
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| discipline | Mathematik |
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| id | DE-604.BV020032461 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:11:18Z |
| institution | BVB |
| isbn | 0817643826 0817644075 9780817643829 0817644423 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013353655 |
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| physical | XXII, 465 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
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| publisher | Birkhäuser |
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| series2 | Cornerstones |
| spelling | Knapp, Anthony W. 1941- Verfasser (DE-588)132959690 aut Advanced real analysis Anthony W. Knapp Boston [u.a.] Birkhäuser 2005 XXII, 465 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cornerstones Erg. zu: Knapp, Anthony W.: Basic real analysis Analyse mathématique Reële functies gtt Mathematical analysis Reelle Analysis (DE-588)4627581-2 gnd rswk-swf Reelle Analysis (DE-588)4627581-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013353655&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Knapp, Anthony W. 1941- Advanced real analysis Analyse mathématique Reële functies gtt Mathematical analysis Reelle Analysis (DE-588)4627581-2 gnd |
| subject_GND | (DE-588)4627581-2 |
| title | Advanced real analysis |
| title_auth | Advanced real analysis |
| title_exact_search | Advanced real analysis |
| title_full | Advanced real analysis Anthony W. Knapp |
| title_fullStr | Advanced real analysis Anthony W. Knapp |
| title_full_unstemmed | Advanced real analysis Anthony W. Knapp |
| title_short | Advanced real analysis |
| title_sort | advanced real analysis |
| topic | Analyse mathématique Reële functies gtt Mathematical analysis Reelle Analysis (DE-588)4627581-2 gnd |
| topic_facet | Analyse mathématique Reële functies Mathematical analysis Reelle Analysis |
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