The theory of Fourier series and integrals:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester u.a.
Wiley
1986
|
| Schriftenreihe: | A Wiley-Interscience publication
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 192 S. graph. Darst. |
| ISBN: | 0471901121 |
Internformat
MARC
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| 100 | 1 | |a Walker, Peter L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The theory of Fourier series and integrals |c P. L. Walker |
| 264 | 1 | |a Chichester u.a. |b Wiley |c 1986 | |
| 300 | |a VIII, 192 S. |b graph. Darst. | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface vii
Chapter 1 Fourier Coefficients and Fourier Series 1
1.1 Introduction 1
1.2 FC functions and their Fourier coefficients 3
1.3 Completeness 12
1.4 Mean square approximation 18
1.5 Convolution 22
Exercises 27
Chapter 2 Convergence Theory 29
2.1 Pointwise convergence 29
2.2 Uniform convergence 35
2.3 Behaviour near discontinuities 37
2.4 Piecewise monotone functions 41
2.5 Divergence of Fourier series 49
Exercises 51
Chapter 3 The Dirichlet Problem and the Poisson Integral ... 53
3.1 Harmonic functions 53
3.2 The Dirichlet problem and the Poisson integral 56
3.3 Applications to Fourier series 63
3.4 Harmonic conjugates 66
3.5 The Dirichlet problem in some other regions 71
3.6 Some applications of harmonic functions 79
Exercises 85
Chapter 4 Conjugate Functions and Conjugate Series 89
4.1 Conjugate series 89
4.2 Properties of the conjugate function 96
Exercises 99
v
vi
Chapter 5 The Fourier Integral 101
5.1 Introduction 101
5.2 The Fourier integral 106
5.3 Summability and inversion of the Fourier integral 115
5.4 Square integrable functions 121
5.5 The Dirichlet problem in the upper half plane, and the Hilbert
transform 123
5.6 Some applications of the Fourier integral 131
Exercises 136
Chapter 6 Multiple Fourier Series and Integrals 139
6.1 FC and F V functions of several variables: Fourier coefficients and
series 140
6.2 Convergence of multiple Fourier series 144
6.3 Multiple Fourier integrals 149
Exercises 154
Appendix A Some Results from Elementary Analysis 157
A.I Continuity and differentiation 157
A.2 Integration 160
A.3 Uniform convergence 167
A.4 Double series and integrals 176
Appendix B Some Definite Integrals 184
Appendix C Bibliography and Guide to Further Reading 189
Index 191
|
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| dewey-sort | 3515 42433 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002301076 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:43:39Z |
| institution | BVB |
| isbn | 0471901121 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001512271 |
| oclc_num | 12422111 |
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| physical | VIII, 192 S. graph. Darst. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Wiley |
| record_format | marc |
| series2 | A Wiley-Interscience publication |
| spelling | Walker, Peter L. Verfasser aut The theory of Fourier series and integrals P. L. Walker Chichester u.a. Wiley 1986 VIII, 192 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Wiley-Interscience publication Fourier, Séries de Matematica larpcal Series (Matematica) larpcal Fourier series Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Fourier-Integral (DE-588)4121290-3 gnd rswk-swf Fourier-Reihe (DE-588)4155109-6 gnd rswk-swf Fourier-Reihe (DE-588)4155109-6 s DE-604 Fourier-Integral (DE-588)4121290-3 s Harmonische Analyse (DE-588)4023453-8 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001512271&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Walker, Peter L. The theory of Fourier series and integrals Fourier, Séries de Matematica larpcal Series (Matematica) larpcal Fourier series Harmonische Analyse (DE-588)4023453-8 gnd Fourier-Integral (DE-588)4121290-3 gnd Fourier-Reihe (DE-588)4155109-6 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4121290-3 (DE-588)4155109-6 |
| title | The theory of Fourier series and integrals |
| title_auth | The theory of Fourier series and integrals |
| title_exact_search | The theory of Fourier series and integrals |
| title_full | The theory of Fourier series and integrals P. L. Walker |
| title_fullStr | The theory of Fourier series and integrals P. L. Walker |
| title_full_unstemmed | The theory of Fourier series and integrals P. L. Walker |
| title_short | The theory of Fourier series and integrals |
| title_sort | the theory of fourier series and integrals |
| topic | Fourier, Séries de Matematica larpcal Series (Matematica) larpcal Fourier series Harmonische Analyse (DE-588)4023453-8 gnd Fourier-Integral (DE-588)4121290-3 gnd Fourier-Reihe (DE-588)4155109-6 gnd |
| topic_facet | Fourier, Séries de Matematica Series (Matematica) Fourier series Harmonische Analyse Fourier-Integral Fourier-Reihe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001512271&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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