An introduction to harmonic analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2004
|
| Ausgabe: | Third edition |
| Schriftenreihe: | Cambridge mathematical library
|
| Schlagworte: | |
| Online-Zugang: | Publisher description Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke - transferred to digital printing 2009 |
| Beschreibung: | xv, 314 Seiten |
| ISBN: | 9780521838290 9780521543590 0521543592 |
Internformat
MARC
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| 100 | 1 | |a Katznelson, Yitzhak |d 1934- |e Verfasser |0 (DE-588)13598291X |4 aut | |
| 245 | 1 | 0 | |a An introduction to harmonic analysis |c Yitzhak Katznelson |
| 250 | |a Third edition | ||
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2004 | |
| 300 | |a xv, 314 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Cambridge mathematical library | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke - transferred to digital printing 2009 | ||
| 650 | 4 | |a Analyse harmonique | |
| 650 | 7 | |a Harmonische analyse |2 gtt | |
| 650 | 4 | |a Harmonic analysis | |
| 650 | 0 | 7 | |a Harmonische Analyse |0 (DE-588)4023453-8 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4151278-9 |a Einführung |2 gnd-content | |
| 689 | 0 | 0 | |a Harmonische Analyse |0 (DE-588)4023453-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | |u http://www.loc.gov/catdir/description/dover033/76003075.html |3 Publisher description | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-012831615 | ||
Datensatz im Suchindex
| _version_ | 1804132805739806720 |
|---|---|
| adam_text | Contents
I Fourier Series on
Τ
1
1
Fourier coefficients
..................... 2
2
Summability in norm and homogeneous banach
spaces on
Τ
......................... 9
3
Pointwise convergence of
ση(
ƒ)............... 18
4
The order of magnitude of Fourier coefficients
...... 23
5
Fourier series of square summable functions
....... 29
6
Absolutely convergent Fourier series
........... 33
7
Fourier coefficients of linear functionals
......... 37
8
Additional comments and applications
.......... 51
*9 The d-dimensional torus
................. 63
II The Convergence of Fourier Series
67
1
Convergence in norm
.................... 67
2
Convergence and divergence at a point
.......... 72
*3 Sets of divergence
...................... 76
III The Conjugate Function
83
1
The conjugate function
................... 83
2
The maximal function of Hardy and Littlewood
..... 96
3
The Hardy spaces
...................... 105
IV Interpolation of Linear Operators
117
1
Interpolation of norms and of linear operators
...... 117
2
The theorem of Hausdorff-Young
............. 123
3
Marcinkiewicz s theorem
.................. 128
V Lacunary Series and Quasi-analytic Classes
133
1
Lacunary series
.......................133
*2 Quasi-analytic classes
................... . 142
vii
VI Fourier Transforms on the Line
151
1
Fourier transforms for L1(M)
................152
2
Fourier-Stieltjes transforms
................163
3
Fourier transforms in LP(R),
1 <
ρ
< 2..........174
4
Tempered distributions and pseudomeasures
.......181
5
Almost-Periodic functions on the line
..........191
6
The weak-star spectrum of bounded functions
......205
7
The Paley-Wiener theorems
................208
*8 The Fourier-Carleman transform
.............214
9
Kronecker s theorem
....................217
VII
Fourier Analysis on Locally Compact
Abelian Groups
223
1
Locally compact abelian groups
.............. 223
2
The
Haar
measure
..................... 224
3
Characters and the dual group
............... 225
4
Fourier transforms
..................... 227
5
Almost-periodic functions and the Bohr
compactification
....................... 229
VIII
Commutative Banach Algebras
231
1
Definition, examples, and elementary properties
.....231
2
Maximal ideals and multiplicative
linear functionals
......................235
3
The maximal-ideal space and the
Gelfand representation
...................242
4
Homomorphisms of Banach algebras
...........251
5
Regular algebras
.......................258
6
Wiener s general Tauberian theorem
............264
7
Spectral synthesis in regular algebras
...........267
8
Functions that operate in regular
Banach algebras
.......................273
9
The algebra M(T) and functions that operate on
Fourier-Stieltjes coefficients
...............282
10
The use of tensor products
.................287
A Vector-Valued Functions
295
1
Riemann integration
....................295
2
Improper integrals
......................296
3
More general integrals
...................296
4
Holomorphic vector-valued functions
...........296
В
Probabilistic Methods
299
1
Random series
........................299
2
Fourier coefficients of continuous functions
.......302
3
Paley-Zygmund, (when
Σ αη 2 = οο)
..........303
Bibliography
307
Index
311
|
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| classification_tum | MAT 420f |
| ctrlnum | (OCoLC)53330817 (DE-599)BVBBV019368076 |
| dewey-full | 515/.2433 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.2433 |
| dewey-search | 515/.2433 |
| dewey-sort | 3515 42433 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Third edition |
| format | Book |
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| id | DE-604.BV019368076 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:58:40Z |
| institution | BVB |
| isbn | 9780521838290 9780521543590 0521543592 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012831615 |
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| physical | xv, 314 Seiten |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Cambridge University Press |
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| series2 | Cambridge mathematical library |
| spelling | Katznelson, Yitzhak 1934- Verfasser (DE-588)13598291X aut An introduction to harmonic analysis Yitzhak Katznelson Third edition Cambridge Cambridge University Press 2004 xv, 314 Seiten txt rdacontent n rdamedia nc rdacarrier Cambridge mathematical library Hier auch später erschienene, unveränderte Nachdrucke - transferred to digital printing 2009 Analyse harmonique Harmonische analyse gtt Harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Harmonische Analyse (DE-588)4023453-8 s DE-604 http://www.loc.gov/catdir/description/dover033/76003075.html Publisher description Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012831615&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Katznelson, Yitzhak 1934- An introduction to harmonic analysis Analyse harmonique Harmonische analyse gtt Harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4151278-9 |
| title | An introduction to harmonic analysis |
| title_auth | An introduction to harmonic analysis |
| title_exact_search | An introduction to harmonic analysis |
| title_full | An introduction to harmonic analysis Yitzhak Katznelson |
| title_fullStr | An introduction to harmonic analysis Yitzhak Katznelson |
| title_full_unstemmed | An introduction to harmonic analysis Yitzhak Katznelson |
| title_short | An introduction to harmonic analysis |
| title_sort | an introduction to harmonic analysis |
| topic | Analyse harmonique Harmonische analyse gtt Harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Analyse harmonique Harmonische analyse Harmonic analysis Harmonische Analyse Einführung |
| url | http://www.loc.gov/catdir/description/dover033/76003075.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012831615&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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