A first course in harmonic analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2005
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | BTU01 TUM01 UBA01 UBR01 UBT01 UPA01 Volltext Inhaltsverzeichnis |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9780387275611 |
| DOI: | 10.1007/0-387-27561-4 |
Internformat
MARC
| LEADER | 00000nmm a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV022375688 | ||
| 003 | DE-604 | ||
| 005 | 20180314 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 070403s2005 |||| o||u| ||||||eng d | ||
| 020 | |a 9780387275611 |c Online |9 978-0-387-27561-1 | ||
| 024 | 7 | |a 10.1007/0-387-27561-4 |2 doi | |
| 035 | |a (OCoLC)612578829 | ||
| 035 | |a (DE-599)BVBBV022375688 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-739 |a DE-355 |a DE-634 |a DE-91 |a DE-384 |a DE-703 |a DE-83 | ||
| 084 | |a SK 450 |0 (DE-625)143240: |2 rvk | ||
| 084 | |a MAT 420f |2 stub | ||
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Deitmar, Anton |d 1960- |e Verfasser |0 (DE-588)103439682X |4 aut | |
| 245 | 1 | 0 | |a A first course in harmonic analysis |c Anton Deitmar |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY |b Springer |c 2005 | |
| 300 | |a 1 Online-Ressource | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Universitext | |
| 650 | 0 | 7 | |a Harmonische Analyse |0 (DE-588)4023453-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Harmonische Analyse |0 (DE-588)4023453-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 0-387-22837-3 |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-0-387-22837-2 |
| 856 | 4 | 0 | |u https://doi.org/10.1007/0-387-27561-4 |x Verlag |3 Volltext |
| 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=015584770&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 912 | |a ZDB-2-SMA | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-015584770 | ||
| 966 | e | |u https://doi.org/10.1007/0-387-27561-4 |l BTU01 |p ZDB-2-SMA |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1007/0-387-27561-4 |l TUM01 |p ZDB-2-SMA |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1007/0-387-27561-4 |l UBA01 |p ZDB-2-SMA |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1007/0-387-27561-4 |l UBR01 |p ZDB-2-SMA |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1007/0-387-27561-4 |l UBT01 |p ZDB-2-SMA |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1007/0-387-27561-4 |l UPA01 |p ZDB-2-SMA |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804136430114439168 |
|---|---|
| adam_text | Contents
I Fourier Analysis 3
1 Fourier Series 5
1.1 Periodic Functions 5
1.2 Exponentials 7
1.3 The Bessel Inequality 9
1.4 Convergence in the L2 Norm 10
1.5 Uniform Convergence of Fourier Series 17
1.6 Periodic Functions Revisited 19
1.7 Exercises 19
2 Hilbert Spaces 25
2.1 Pre Hilbert and Hilbert Spaces 25
2.2 £2 Spaces 29
2.3 Orthonormal Bases and Completion 31
2.4 Fourier Series Revisited 36
2.5 Exercises 37
3 The Fourier Transform 41
3.1 Convergence Theorems 41
3.2 Convolution 43
3.3 The Transform 46
ix
x CONTENTS
3.4 The Inversion Formula 49
3.5 Plancherel s Theorem 52
3.6 The Poisson Summation Formula 54
3.7 Theta Series 56
3.8 Exercises 56
4 Distributions 59
4.1 Definition 59
4.2 The Derivative of a Distribution 61
4.3 Tempered Distributions 62
4.4 Fourier Transform 65
4.5 Exercises 68
II LCA Groups 71
5 Finite Abelian Groups 73
5.1 The Dual Group 73
5.2 The Fourier Transform 75
5.3 Convolution 77
5.4 Exercises 78
6 LCA Groups 81
6.1 Metric Spaces and Topology 81
6.2 Completion 89
6.3 LCA Groups 94
6.4 Exercises 96
7 The Dual Group 101
7.1 The Dual as LCA Group 101
CONTENTS xi
7.2 Pontryagin Duality 107
7.3 Exercises 108
8 Plancherel Theorem 111
8.1 Haar Integration Ill
8.2 Fubini s Theorem 116
8.3 Convolution 120
8.4 Plancherel s Theorem 122
8.5 Exercises 125
III Noncommutative Groups 127
9 Matrix Groups 129
9.1 GL,,(C) and U(n) 129
9.2 Representations 131
9.3 The Exponential 133
9.4 Exercises 138
10 The Representations of SU(2) 141
10.1 The Lie Algebra 142
10.2 The Representations 146
10.3 Exercises 147
11 The Peter Weyl Theorem 149
11.1 Decomposition of Representations 149
11.2 The Representation on Hom(Vv VT) 150
11.3 The Peter Weyl Theorem 151
11.4 A Reformulation 154
11.5 Exercises 155
xii CONTENTS
12 The Heisenberg Group 157
12.1 Definition 157
12.2 The Unitary Dual 158
12.3 Hilbert Schmidt Operators 162
12.4 The Plancherel Theorem for U 167
12.5 A Reformulation 169
12.6 Exercises 173
A The Riemann Zeta Function 175
B Haar Integration 179
Bibiliography 187
Index 190
|
| adam_txt |
Contents
I Fourier Analysis 3
1 Fourier Series 5
1.1 Periodic Functions 5
1.2 Exponentials 7
1.3 The Bessel Inequality 9
1.4 Convergence in the L2 Norm 10
1.5 Uniform Convergence of Fourier Series 17
1.6 Periodic Functions Revisited 19
1.7 Exercises 19
2 Hilbert Spaces 25
2.1 Pre Hilbert and Hilbert Spaces 25
2.2 £2 Spaces 29
2.3 Orthonormal Bases and Completion 31
2.4 Fourier Series Revisited 36
2.5 Exercises 37
3 The Fourier Transform 41
3.1 Convergence Theorems 41
3.2 Convolution 43
3.3 The Transform 46
ix
x CONTENTS
3.4 The Inversion Formula 49
3.5 Plancherel's Theorem 52
3.6 The Poisson Summation Formula 54
3.7 Theta Series 56
3.8 Exercises 56
4 Distributions 59
4.1 Definition 59
4.2 The Derivative of a Distribution 61
4.3 Tempered Distributions 62
4.4 Fourier Transform 65
4.5 Exercises 68
II LCA Groups 71
5 Finite Abelian Groups 73
5.1 The Dual Group 73
5.2 The Fourier Transform 75
5.3 Convolution 77
5.4 Exercises 78
6 LCA Groups 81
6.1 Metric Spaces and Topology 81
6.2 Completion 89
6.3 LCA Groups 94
6.4 Exercises 96
7 The Dual Group 101
7.1 The Dual as LCA Group 101
CONTENTS xi
7.2 Pontryagin Duality 107
7.3 Exercises 108
8 Plancherel Theorem 111
8.1 Haar Integration Ill
8.2 Fubini's Theorem 116
8.3 Convolution 120
8.4 Plancherel's Theorem 122
8.5 Exercises 125
III Noncommutative Groups 127
9 Matrix Groups 129
9.1 GL,,(C) and U(n) 129
9.2 Representations 131
9.3 The Exponential 133
9.4 Exercises 138
10 The Representations of SU(2) 141
10.1 The Lie Algebra 142
10.2 The Representations 146
10.3 Exercises 147
11 The Peter Weyl Theorem 149
11.1 Decomposition of Representations 149
11.2 The Representation on Hom(Vv VT) 150
11.3 The Peter Weyl Theorem 151
11.4 A Reformulation 154
11.5 Exercises 155
xii CONTENTS
12 The Heisenberg Group 157
12.1 Definition 157
12.2 The Unitary Dual 158
12.3 Hilbert Schmidt Operators 162
12.4 The Plancherel Theorem for U 167
12.5 A Reformulation 169
12.6 Exercises 173
A The Riemann Zeta Function 175
B Haar Integration 179
Bibiliography 187
Index 190 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Deitmar, Anton 1960- |
| author_GND | (DE-588)103439682X |
| author_facet | Deitmar, Anton 1960- |
| author_role | aut |
| author_sort | Deitmar, Anton 1960- |
| author_variant | a d ad |
| building | Verbundindex |
| bvnumber | BV022375688 |
| classification_rvk | SK 450 |
| classification_tum | MAT 420f MAT 000 |
| collection | ZDB-2-SMA |
| ctrlnum | (OCoLC)612578829 (DE-599)BVBBV022375688 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| doi_str_mv | 10.1007/0-387-27561-4 |
| edition | 2. ed. |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02167nmm a2200493 c 4500</leader><controlfield tag="001">BV022375688</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20180314 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">070403s2005 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780387275611</subfield><subfield code="c">Online</subfield><subfield code="9">978-0-387-27561-1</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/0-387-27561-4</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)612578829</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV022375688</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-83</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 420f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Deitmar, Anton</subfield><subfield code="d">1960-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)103439682X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A first course in harmonic analysis</subfield><subfield code="c">Anton Deitmar</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, NY</subfield><subfield code="b">Springer</subfield><subfield code="c">2005</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource</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">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Universitext</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="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="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">0-387-22837-3</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">978-0-387-22837-2</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/0-387-27561-4</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</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=015584770&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-015584770</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1007/0-387-27561-4</subfield><subfield code="l">BTU01</subfield><subfield code="p">ZDB-2-SMA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1007/0-387-27561-4</subfield><subfield code="l">TUM01</subfield><subfield code="p">ZDB-2-SMA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1007/0-387-27561-4</subfield><subfield code="l">UBA01</subfield><subfield code="p">ZDB-2-SMA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1007/0-387-27561-4</subfield><subfield code="l">UBR01</subfield><subfield code="p">ZDB-2-SMA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1007/0-387-27561-4</subfield><subfield code="l">UBT01</subfield><subfield code="p">ZDB-2-SMA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1007/0-387-27561-4</subfield><subfield code="l">UPA01</subfield><subfield code="p">ZDB-2-SMA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV022375688 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T17:09:09Z |
| indexdate | 2024-07-09T20:56:16Z |
| institution | BVB |
| isbn | 9780387275611 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015584770 |
| oclc_num | 612578829 |
| open_access_boolean | |
| owner | DE-739 DE-355 DE-BY-UBR DE-634 DE-91 DE-BY-TUM DE-384 DE-703 DE-83 |
| owner_facet | DE-739 DE-355 DE-BY-UBR DE-634 DE-91 DE-BY-TUM DE-384 DE-703 DE-83 |
| physical | 1 Online-Ressource |
| psigel | ZDB-2-SMA |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Deitmar, Anton 1960- Verfasser (DE-588)103439682X aut A first course in harmonic analysis Anton Deitmar 2. ed. New York, NY Springer 2005 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Universitext Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s DE-604 Erscheint auch als Druckausgabe 0-387-22837-3 Erscheint auch als Druckausgabe 978-0-387-22837-2 https://doi.org/10.1007/0-387-27561-4 Verlag Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015584770&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Deitmar, Anton 1960- A first course in harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4023453-8 |
| title | A first course in harmonic analysis |
| title_auth | A first course in harmonic analysis |
| title_exact_search | A first course in harmonic analysis |
| title_exact_search_txtP | A first course in harmonic analysis |
| title_full | A first course in harmonic analysis Anton Deitmar |
| title_fullStr | A first course in harmonic analysis Anton Deitmar |
| title_full_unstemmed | A first course in harmonic analysis Anton Deitmar |
| title_short | A first course in harmonic analysis |
| title_sort | a first course in harmonic analysis |
| topic | Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Harmonische Analyse |
| url | https://doi.org/10.1007/0-387-27561-4 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015584770&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT deitmaranton afirstcourseinharmonicanalysis |