Fourier series:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English German |
| Veröffentlicht: |
New York
Chelsea Publ. Co.
1959
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Einheitssacht.: Fouriersche Reihen <engl.> |
| Beschreibung: | 176 S. |
Internformat
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV021916943 | ||
| 003 | DE-604 | ||
| 005 | 20040301000000.0 | ||
| 007 | t | ||
| 008 | 940307s1959 |||| 00||| eng d | ||
| 035 | |a (OCoLC)546049 | ||
| 035 | |a (DE-599)BVBBV021916943 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | 1 | |a eng |h ger | |
| 049 | |a DE-706 | ||
| 050 | 0 | |a QA404 | |
| 082 | 0 | |a 517.35 | |
| 084 | |a SK 450 |0 (DE-625)143240: |2 rvk | ||
| 100 | 1 | |a Rogosinski, Werner W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fourier series |c by Werner Rogosinski |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York |b Chelsea Publ. Co. |c 1959 | |
| 300 | |a 176 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Einheitssacht.: Fouriersche Reihen <engl.> | ||
| 650 | 4 | |a Fourier series | |
| 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 |
| 689 | 0 | 0 | |a Fourier-Reihe |0 (DE-588)4155109-6 |D s |
| 689 | 0 | 1 | |a Harmonische Analyse |0 (DE-588)4023453-8 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015132114&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-015132114 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804135868621914112 |
|---|---|
| adam_text | TABLE OF CONTENTS
Translators preface iii
I. Introduction to the Problem
§ 1. The vibrating string (statement of the
problem) 1
§ 2. Trigonometric series 4
§ 3. Fourier series 8
§ 4. The closure theorem 11
§ 5. Some examples 15
II. Representation Theory
§ 1. Theorems on Fourier coefficients 21
§ 2. The integration of Fourier series 26
§ 3. A representation theorem 30
§ 4. Examples 33
§ 5. The vibrating string (solution) 39
§ 6. The Weierstrass approximation theorem 46
III. The Completeness Theorem
§ 1. A minimal property of partial sums of
Fourier series 50
§ 2. The completeness theorem 53
§ 3. Parseval s formula 58
§ 4. Application to the Isoperimetric problem. 61
IV. Convergence Theory
§ 1. Dirichlet s formula 64
§ 2. Riemann s theorem 66
v
vi Table of Contents
§ 3. Dini s criterion 68
§ 4. The Dirichlet Jordan criterion 72
§5. The Fourier series at ordinary points. ... 75
§ 6. The conjugate series 82
V. Some Applications
§ 1. The Fourier integral theorem 88
§ 2. Summation formulas 95
§ 3. Stirling s formula 99
VI. Divergent Fourier Series
§ 1. Mean value methods 103
§ 2. Fejer means Ill
§ 3. The Abel Poisson method 118
§ 4. The Lebesgue and Riemann methods.. . .122
§ 5. Another method of summation 128
§ 6. The Gibbs phenomenon 135
VII. Uniqueness Theorems
§ 1. A theorem of Schwarz in the differential
calculus 141
§ 2. The Heine Cantor theorem 144
§ 3. A theorem of Arzela and Lebesgue in the
integral calculus 149
§ 4. The DuBois Reymond theorem 154
Appendix 160
Bibliography 171
Index 173
|
| adam_txt |
TABLE OF CONTENTS
Translators' preface iii
I. Introduction to the Problem
§ 1. The vibrating string (statement of the
problem) 1
§ 2. Trigonometric series 4
§ 3. Fourier series 8
§ 4. The closure theorem 11
§ 5. Some examples 15
II. Representation Theory
§ 1. Theorems on Fourier coefficients 21
§ 2. The integration of Fourier series 26
§ 3. A representation theorem 30
§ 4. Examples 33
§ 5. The vibrating string (solution) 39
§ 6. The Weierstrass approximation theorem 46
III. The Completeness Theorem
§ 1. A minimal property of partial sums of
Fourier series 50
§ 2. The completeness theorem 53
§ 3. Parseval's formula 58
§ 4. Application to the Isoperimetric problem. 61
IV. Convergence Theory
§ 1. Dirichlet's formula 64
§ 2. Riemann's theorem 66
v
vi Table of Contents
§ 3. Dini's criterion 68
§ 4. The Dirichlet Jordan criterion 72
§5. The Fourier series at ordinary points. . 75
§ 6. The conjugate series 82
V. Some Applications
§ 1. The Fourier integral theorem 88
§ 2. Summation formulas 95
§ 3. Stirling's formula 99
VI. Divergent Fourier Series
§ 1. Mean value methods 103
§ 2. Fejer means Ill
§ 3. The Abel Poisson method 118
§ 4. The Lebesgue and Riemann methods. . .122
§ 5. Another method of summation 128
§ 6. The Gibbs phenomenon 135
VII. Uniqueness Theorems
§ 1. A theorem of Schwarz in the differential
calculus 141
§ 2. The Heine Cantor theorem 144
§ 3. A theorem of Arzela and Lebesgue in the
integral calculus 149
§ 4. The DuBois Reymond theorem 154
Appendix 160
Bibliography 171
Index 173 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Rogosinski, Werner W. |
| author_facet | Rogosinski, Werner W. |
| author_role | aut |
| author_sort | Rogosinski, Werner W. |
| author_variant | w w r ww wwr |
| building | Verbundindex |
| bvnumber | BV021916943 |
| 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 |
| ctrlnum | (OCoLC)546049 (DE-599)BVBBV021916943 |
| dewey-full | 517.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 517 - [Unassigned] |
| dewey-raw | 517.35 |
| dewey-search | 517.35 |
| dewey-sort | 3517.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01440nam a2200397zc 4500</leader><controlfield tag="001">BV021916943</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20040301000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">940307s1959 |||| 00||| eng d</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)546049</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV021916943</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield></datafield><datafield tag="041" ind1="1" ind2=" "><subfield code="a">eng</subfield><subfield code="h">ger</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-706</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA404</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">517.35</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="100" ind1="1" ind2=" "><subfield code="a">Rogosinski, Werner W.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Fourier series</subfield><subfield code="c">by Werner Rogosinski</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York</subfield><subfield code="b">Chelsea Publ. Co.</subfield><subfield code="c">1959</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">176 S.</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="500" ind1=" " ind2=" "><subfield code="a">Einheitssacht.: Fouriersche Reihen <engl.></subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fourier series</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="689" ind1="0" 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="0" ind2="1"><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="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ 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=015132114&sequence=000002&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:BVB01-015132114</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></record></collection> |
| id | DE-604.BV021916943 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:05:33Z |
| indexdate | 2024-07-09T20:47:21Z |
| institution | BVB |
| language | English German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015132114 |
| oclc_num | 546049 |
| open_access_boolean | |
| owner | DE-706 |
| owner_facet | DE-706 |
| physical | 176 S. |
| publishDate | 1959 |
| publishDateSearch | 1959 |
| publishDateSort | 1959 |
| publisher | Chelsea Publ. Co. |
| record_format | marc |
| spelling | Rogosinski, Werner W. Verfasser aut Fourier series by Werner Rogosinski 2. ed. New York Chelsea Publ. Co. 1959 176 S. txt rdacontent n rdamedia nc rdacarrier Einheitssacht.: Fouriersche Reihen <engl.> Fourier series Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Fourier-Reihe (DE-588)4155109-6 gnd rswk-swf Fourier-Reihe (DE-588)4155109-6 s Harmonische Analyse (DE-588)4023453-8 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015132114&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rogosinski, Werner W. Fourier series Fourier series Harmonische Analyse (DE-588)4023453-8 gnd Fourier-Reihe (DE-588)4155109-6 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4155109-6 |
| title | Fourier series |
| title_auth | Fourier series |
| title_exact_search | Fourier series |
| title_exact_search_txtP | Fourier series |
| title_full | Fourier series by Werner Rogosinski |
| title_fullStr | Fourier series by Werner Rogosinski |
| title_full_unstemmed | Fourier series by Werner Rogosinski |
| title_short | Fourier series |
| title_sort | fourier series |
| topic | Fourier series Harmonische Analyse (DE-588)4023453-8 gnd Fourier-Reihe (DE-588)4155109-6 gnd |
| topic_facet | Fourier series Harmonische Analyse Fourier-Reihe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015132114&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rogosinskiwernerw fourierseries |