Fourier series and integral transforms:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1997
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 189 S. graph. Darst. |
| ISBN: | 0521592097 0521597714 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV011537318 | ||
| 003 | DE-604 | ||
| 005 | 20000804 | ||
| 007 | t | ||
| 008 | 970917s1997 d||| |||| 00||| eng d | ||
| 020 | |a 0521592097 |9 0-521-59209-7 | ||
| 020 | |a 0521597714 |9 0-521-59771-4 | ||
| 035 | |a (OCoLC)36083629 | ||
| 035 | |a (DE-599)BVBBV011537318 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-29T |a DE-739 |a DE-703 |a DE-898 |a DE-355 |a DE-384 |a DE-91G |a DE-11 |a DE-188 |a DE-B768 | ||
| 050 | 0 | |a QA404 | |
| 082 | 0 | |a 515/.723 |2 21 | |
| 084 | |a SK 450 |0 (DE-625)143240: |2 rvk | ||
| 084 | |a MAT 440f |2 stub | ||
| 084 | |a MAT 420f |2 stub | ||
| 100 | 1 | |a Pinkus, Allan |d 1946- |e Verfasser |0 (DE-588)110369297 |4 aut | |
| 245 | 1 | 0 | |a Fourier series and integral transforms |c Allan Pinkus & Samy Zafrany |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1997 | |
| 300 | |a VII, 189 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Análise de fourier (análise) |2 larpcal | |
| 650 | 4 | |a Fourier, Séries de | |
| 650 | 7 | |a Fourier, Séries de |2 ram | |
| 650 | 4 | |a Transformations intégrales | |
| 650 | 4 | |a Fourier series | |
| 650 | 4 | |a Integral transforms | |
| 650 | 0 | 7 | |a Fourier-Transformation |0 (DE-588)4018014-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Harmonische Analyse |0 (DE-588)4023453-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Fourier-Reihe |0 (DE-588)4155109-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Laplace-Transformation |0 (DE-588)4034577-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Harmonische Analyse |0 (DE-588)4023453-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Fourier-Transformation |0 (DE-588)4018014-1 |D s |
| 689 | 1 | |8 1\p |5 DE-604 | |
| 689 | 2 | 0 | |a Laplace-Transformation |0 (DE-588)4034577-4 |D s |
| 689 | 2 | |8 2\p |5 DE-604 | |
| 689 | 3 | 0 | |a Fourier-Reihe |0 (DE-588)4155109-6 |D s |
| 689 | 3 | |8 3\p |5 DE-604 | |
| 700 | 1 | |a Zafrany, Samy |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m SWB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007765778&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007765778 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 3\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804126059445092352 |
|---|---|
| adam_text | IMAGE 1
V
CONTENTS
PREFACE VII
O NOTADON AND TERMINOLOGY 1
1 BASICCONCEPTS IN SETTHEORY 1
2 CALCULUS NOTATION 2
3 USEFULTRIGONOMETRIC FORMULAE 4
1 BACKGROUND: INNER PRODUCT SPACES 5
O INTRODUCTION 5
1 LINEAR AND INNER PRODUCT SPACES 5
2 THE NORM 10
3 ORTHOGONAL AND ORTHONORMAL SYSTEMS 15
4 ORTHOGONAL PROJECTIONS AND APPROXIMATION IN THE MEAN 19
5 INFINITE ORTHONORMAL SYSTEMS 24
REVIEWEXERCISES 30
2 FOURIER SERIES 32
O INTRODUCTION 32
1 DEFINITIONS 32
2 EVENNESS, ODDNESS, AND ADDITIONAL EXAMPLES 40 3 COMPLEX FOURIER SERIES
42
4 POINTWISE CONVERGENCE AND DIRICHLET STHEOREM 46 5 UNIFORM CONVERGENCE
56
6 PARSEVAL SIDENTITY 63
7 THE GIBBS PHENOMENON 68
8 SINE AND COSINE SERIES 72
9 DIFFERENTIATION AND INTEGRATION OFFOURIER SERIES 76 10 FOURIER SERIES
ON OTHER INTERVALS 81
11 APPLICATIONS TO PARTIAL DIFFERENTIALEQUATIONS 85 REVIEWEXERCISES 89
3 THE FOURIER TRANSFORM 93
O INTRODUCTION 93
1 DEFINITIONS AND BASICPROPERTIES 93
IMAGE 2
VI
2 EXAMPLES 98
3 PROPERTIES AND FORMULAE 102
4 THE INVERSE FOURIER TRANSFORM AND PLANCHEREL S IDENTITY 108
5 CONVOLUTION 116
6 APPLICATIONS OFTHE RESIDUE THEOREM 119
7 APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS 125 8 APPLICATIONS TO
SIGNALPROCESSING 130
REVIEWEXERCISES ...................................... 137
4 THE LAPLACE TRANSFORM 140
O INTRODUCTION 140
1 DEFINITION AND EXAMPLES 140
2 MOREFORMULAE AND EXAMPLES 143
3 APPLICATIONS TO ORDINARY DIFFERENTIAL EQUATIONS 149 4 THE HEAVISIDE
AND DIRAC-DELTA FUNCTIONS 155
5 CONVOLUTION ................. 162
6 MORE EXAMPLES AND APPLICATIONS 168
7 THE INVERSE TRANSFORM FORMULA 173
8 APPLICATIONS OFTHE INVERSE TRANSFORM 175
REVIEWEXERCISES ...................................... 180
APPENDIXA: THE RESIDUE THEOREM AND RELATED RESULTS .. 182
APPENDIX B: LELBNLZ S RULE AND FUBLNL S THEOREM 186
INDEX 188
|
| any_adam_object | 1 |
| author | Pinkus, Allan 1946- Zafrany, Samy |
| author_GND | (DE-588)110369297 |
| author_facet | Pinkus, Allan 1946- Zafrany, Samy |
| author_role | aut aut |
| author_sort | Pinkus, Allan 1946- |
| author_variant | a p ap s z sz |
| building | Verbundindex |
| bvnumber | BV011537318 |
| callnumber-first | Q - Science |
| callnumber-label | QA404 |
| callnumber-raw | QA404 |
| callnumber-search | QA404 |
| callnumber-sort | QA 3404 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 450 |
| classification_tum | MAT 440f MAT 420f |
| ctrlnum | (OCoLC)36083629 (DE-599)BVBBV011537318 |
| dewey-full | 515/.723 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.723 |
| dewey-search | 515/.723 |
| dewey-sort | 3515 3723 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02471nam a2200613 c 4500</leader><controlfield tag="001">BV011537318</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20000804 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">970917s1997 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0521592097</subfield><subfield code="9">0-521-59209-7</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0521597714</subfield><subfield code="9">0-521-59771-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)36083629</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV011537318</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-29T</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-898</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-B768</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA404</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.723</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 450</subfield><subfield code="0">(DE-625)143240:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 440f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 420f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Pinkus, Allan</subfield><subfield code="d">1946-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)110369297</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Fourier series and integral transforms</subfield><subfield code="c">Allan Pinkus & Samy Zafrany</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1. publ.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge [u.a.]</subfield><subfield code="b">Cambridge Univ. Press</subfield><subfield code="c">1997</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VII, 189 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Análise de fourier (análise)</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fourier, Séries de</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Fourier, Séries de</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Transformations intégrales</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fourier series</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Integral transforms</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Fourier-Transformation</subfield><subfield code="0">(DE-588)4018014-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Harmonische Analyse</subfield><subfield code="0">(DE-588)4023453-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Fourier-Reihe</subfield><subfield code="0">(DE-588)4155109-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Laplace-Transformation</subfield><subfield code="0">(DE-588)4034577-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Harmonische Analyse</subfield><subfield code="0">(DE-588)4023453-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Fourier-Transformation</subfield><subfield code="0">(DE-588)4018014-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Laplace-Transformation</subfield><subfield code="0">(DE-588)4034577-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="3" ind2="0"><subfield code="a">Fourier-Reihe</subfield><subfield code="0">(DE-588)4155109-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="3" ind2=" "><subfield code="8">3\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zafrany, Samy</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">SWB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007765778&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-007765778</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">3\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV011537318 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:11:26Z |
| institution | BVB |
| isbn | 0521592097 0521597714 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007765778 |
| oclc_num | 36083629 |
| open_access_boolean | |
| owner | DE-29T DE-739 DE-703 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-384 DE-91G DE-BY-TUM DE-11 DE-188 DE-B768 |
| owner_facet | DE-29T DE-739 DE-703 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-384 DE-91G DE-BY-TUM DE-11 DE-188 DE-B768 |
| physical | VII, 189 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Pinkus, Allan 1946- Verfasser (DE-588)110369297 aut Fourier series and integral transforms Allan Pinkus & Samy Zafrany 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1997 VII, 189 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Análise de fourier (análise) larpcal Fourier, Séries de Fourier, Séries de ram Transformations intégrales Fourier series Integral transforms Fourier-Transformation (DE-588)4018014-1 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Fourier-Reihe (DE-588)4155109-6 gnd rswk-swf Laplace-Transformation (DE-588)4034577-4 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s DE-604 Fourier-Transformation (DE-588)4018014-1 s 1\p DE-604 Laplace-Transformation (DE-588)4034577-4 s 2\p DE-604 Fourier-Reihe (DE-588)4155109-6 s 3\p DE-604 Zafrany, Samy Verfasser aut SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007765778&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Pinkus, Allan 1946- Zafrany, Samy Fourier series and integral transforms Análise de fourier (análise) larpcal Fourier, Séries de Fourier, Séries de ram Transformations intégrales Fourier series Integral transforms Fourier-Transformation (DE-588)4018014-1 gnd Harmonische Analyse (DE-588)4023453-8 gnd Fourier-Reihe (DE-588)4155109-6 gnd Laplace-Transformation (DE-588)4034577-4 gnd |
| subject_GND | (DE-588)4018014-1 (DE-588)4023453-8 (DE-588)4155109-6 (DE-588)4034577-4 |
| title | Fourier series and integral transforms |
| title_auth | Fourier series and integral transforms |
| title_exact_search | Fourier series and integral transforms |
| title_full | Fourier series and integral transforms Allan Pinkus & Samy Zafrany |
| title_fullStr | Fourier series and integral transforms Allan Pinkus & Samy Zafrany |
| title_full_unstemmed | Fourier series and integral transforms Allan Pinkus & Samy Zafrany |
| title_short | Fourier series and integral transforms |
| title_sort | fourier series and integral transforms |
| topic | Análise de fourier (análise) larpcal Fourier, Séries de Fourier, Séries de ram Transformations intégrales Fourier series Integral transforms Fourier-Transformation (DE-588)4018014-1 gnd Harmonische Analyse (DE-588)4023453-8 gnd Fourier-Reihe (DE-588)4155109-6 gnd Laplace-Transformation (DE-588)4034577-4 gnd |
| topic_facet | Análise de fourier (análise) Fourier, Séries de Transformations intégrales Fourier series Integral transforms Fourier-Transformation Harmonische Analyse Fourier-Reihe Laplace-Transformation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007765778&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT pinkusallan fourierseriesandintegraltransforms AT zafranysamy fourierseriesandintegraltransforms |