Introduction to Fourier analysis on Euclidean spaces:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, NJ
Princeton Univ. Press
1990
|
| Edition: | 6. print. |
| Series: | Princeton mathematical series
32 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 297 S. |
| ISBN: | 069108078X 9780691080789 |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to Fourier analysis on Euclidean spaces |c by Elias M. Stein & Guido Weiss |
| 250 | |a 6. print. | ||
| 264 | 1 | |a Princeton, NJ |b Princeton Univ. Press |c 1990 | |
| 300 | |a X, 297 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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Record in the Search Index
| _version_ | 1804124631159799808 |
|---|---|
| adam_text | Contents
Preface
vii
Chapter I. The Fourier Transform
1
1.
The basic L1 theory of the Fourier transform
1
2.
The I? theory and the Plancherel theorem
16
3.
The class of tempered distributions
19
4.
Further results
31
Chapter II. Boundary Values of Harmonic Functions
37
1.
Basic properties of harmonic functions
37
2.
The characterization of
Poisson
integrals
47
3.
The Hardy-Littlewood maximal function and non-
tangential convergence of harmonic functions
S3
4.
Subharmonic functions and majorization by harmonic
functions
75
5.
Further results
83
Chapter HI. The Theory of H Spaces on Tubes
89
1.
Introductory remarks
89
2.
The H% theory
91
3.
Tubes over cones
101
4.
The Paley-Wiener theorem
108
5.
The H theory
114
6.
Further results
121
Chapter IV. Symmetry Properties of the Fourier Transform
133
1.
Decomposition of L3(Ea) into subspaces invariant
under the Fourier transform
134
2.
Spherical harmonics
137
3.
The action of the Fourier transform on the spaces 4?fc
153
4.
Some applications
159
5.
Further results
172
χ
CONTENTS
Chapter V. Interpolation of Operators
177
1.
The M. Riesz convexity theorem and interpolation of
operators defined on Lp spaces
177
2.
The Marcinkiewicz interpolation theorem
183
3.
L(p, q) spaces
188
4.
Interpolation of analytic families of operators
205
5.
Further results
209
Chapter VI. Singular Integrals and Systems of Conjugate
Harmonic Functions
217
1.
The Hubert transform
217
2.
Singular integral operators with odd kernels
221
3.
Singular integral operators with even kernels
224
4.
W
spaces of conjugate harmonic functions
228
5.
Further results
238
Chapter
VII.
Multiple Fourier Series
245
1.
Elementary properties
245
2.
The
Poisson
summation formula
250
3.
Multiplier transformations
257
4.
Summability below the critical index (negative results)
267
5.
Summability below the critical index
275
6.
Further results
282
Bibliography
287
Index
295
|
| any_adam_object | 1 |
| author | Stein, Elias M. 1931-2018 Weiss, Guido |
| author_GND | (DE-588)119278596 |
| author_facet | Stein, Elias M. 1931-2018 Weiss, Guido |
| author_role | aut aut |
| author_sort | Stein, Elias M. 1931-2018 |
| author_variant | e m s em ems g w gw |
| building | Verbundindex |
| bvnumber | BV010221679 |
| classification_rvk | SK 450 |
| classification_tum | MAT 424f |
| ctrlnum | (OCoLC)257883425 (DE-599)BVBBV010221679 |
| 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 | 6. print. |
| format | Book |
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| id | DE-604.BV010221679 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:48:44Z |
| institution | BVB |
| isbn | 069108078X 9780691080789 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006793169 |
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| physical | X, 297 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Princeton Univ. Press |
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| series | Princeton mathematical series |
| series2 | Princeton mathematical series |
| spelling | Stein, Elias M. 1931-2018 Verfasser (DE-588)119278596 aut Introduction to Fourier analysis on Euclidean spaces by Elias M. Stein & Guido Weiss 6. print. Princeton, NJ Princeton Univ. Press 1990 X, 297 S. txt rdacontent n rdamedia nc rdacarrier Princeton mathematical series 32 Euklidischer Raum (DE-588)4309127-1 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s Euklidischer Raum (DE-588)4309127-1 s 1\p DE-604 Weiss, Guido Verfasser aut Princeton mathematical series 32 (DE-604)BV000019035 32 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006793169&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 | Stein, Elias M. 1931-2018 Weiss, Guido Introduction to Fourier analysis on Euclidean spaces Princeton mathematical series Euklidischer Raum (DE-588)4309127-1 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4309127-1 (DE-588)4023453-8 |
| title | Introduction to Fourier analysis on Euclidean spaces |
| title_auth | Introduction to Fourier analysis on Euclidean spaces |
| title_exact_search | Introduction to Fourier analysis on Euclidean spaces |
| title_full | Introduction to Fourier analysis on Euclidean spaces by Elias M. Stein & Guido Weiss |
| title_fullStr | Introduction to Fourier analysis on Euclidean spaces by Elias M. Stein & Guido Weiss |
| title_full_unstemmed | Introduction to Fourier analysis on Euclidean spaces by Elias M. Stein & Guido Weiss |
| title_short | Introduction to Fourier analysis on Euclidean spaces |
| title_sort | introduction to fourier analysis on euclidean spaces |
| topic | Euklidischer Raum (DE-588)4309127-1 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Euklidischer Raum Harmonische Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006793169&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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