Trigonometric Fourier series and their conjugates
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| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1996
|
| Schriftenreihe: | Mathematics and its applications
372 |
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| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Žižiašvili, Levan |d 1934- |e Verfasser |0 (DE-588)104311355 |4 aut | |
| 245 | 1 | 0 | |a Trigonometric Fourier series and their conjugates |c by Levan Zhizhiashvili |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1996 | |
| 300 | |a XII, 300 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 372 | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 420f 2001 A 36506 |
|---|---|
| DE-BY-TUM_katkey | 773719 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020539179 |
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| adam_text | Table of Contents
Preface xi
Part 1
SIMPLE TRIGONOMETRIC SERIES
Chapter I. The Conjugation Operator and
the Hilbert Transform
1.1. Some Definitions and Well known Results 3
1.2. On the Theorems of Kolmogorov, Titchmarsh and Kober 15
1.3. On a Theorem of Hardy and Littlewood 27
1.4. Unsolved Problems 33
Chapter II. Pointwise Convergence and Summability
of Trigonometric Series
2.1. Some Definitions and Well known Results 35
2.2. Pointwise Convergence and Summability of Fourier Series
and Conjugate Trigonometric Series 43
2.3. On the Divergence Almost Everywhere of Trigonometric
Fourier Series 61
2.4. Unsolved Problems 68
Chapter III. Convergence and Summability of Trigonometric
Fourier Series and Their Conjugates
in the Spaces LP(T), p E]0, +oo[
3.1. Convergence and Summability of the Series r[f] and a[f)
in the Spaces L (T), p e]0,1] 71
3.2. Convergence and Summability of cr[f] and ?[f]
in the Spaces LP(T), p € [1, +oo] 72
3.3. On the Series a[f] and x[f] for Even and Odd / 85
3.4. Unsolved Problems 92
Chapter IV. Some Approximating Properties of Cesaro
Means of the Series a[f] and a[f]
4.1. Approximating Properties of Cesaro Means of a[f] ._. 93
4.2. Approximating Properties of Cesaro Means of the Series a[f] 109
4.3. Unsolved Problems 116
viii
Part 2
MULTIPLE TRIGONOMETRIC SERIES
Chapter I. Conjugate Functions and Hilbert Transforms
of Functions of Several Variables
1.1. Some Definitions and Auxiliary Statements 119
1.2. On Existence of Conjugate Functions and of Hilbert Transforms 132
1.3. Lebesgue Integrability of Conjugate Functions of Several Variables ... 152
1.4. On the Validity of a Theorem of M. Riesz for Functions
of Several Variables 156
1.5. On the Validity of Kolmogorov s Theorem for Conjugate Functions
and Hilbert Transforms of Functions of Several Variables 161
1.6. On Some Conditions of Existence and Integrability
of Conjugate Functions of Several Variables in Terms
of Mixed and Partial Integral Moduli of Continuity 164
1.7. Unsolved Problems 166
Chapter II. Convergence and Summability at a Point or
Almost Everywhere of Multiple Trigonometric
Fourier Series and Their Conjugates
2.1. Convergence and Summability by Multiple Cesaro Method of
Negative Order of the Series rn[f] and Tn[/ B] at Separate
Points or Almost Everywhere 167
2.2. Almost Everywhere Summability of the Series ?„[/, B] by Multiple
Methods of Poisson Abel and Cesaro of Positive Order. Integrability of
Some Majorants Connected with Multiple Series crn[f) and an[/, B] ... 182
2.3. Unsolved Problems 201
Chapter III. Some Approximating Properties of n Fold
Cesaro Means of the Series crn[f] and an[f,B]
3.1. Approximating Properties of n Fold Cesaro Means
of the Series an[f) 205
3.2. Approximating Properties of n fold Cesaro Means
of the Series an[f, B] 223
3.3. Unsolved Problems 224
Chapter IV. Convergence and Summability of Multiple
Trigonometric Fourier Series and Their
Conjugates in the Spaces Lp(Tn), p e]0,+oo]
4.1. Convergence and Summability of the Series rn[f] and an[f,B]
in the Spaces V{Tn), p £ ]0,1] 225
4.2. Convergence and Summability of the Series an[f] and cn[f, B]
in the Spaces Lp(Tn), p G [1, +oo] 230
4.3. Unsolved Problems 241
ix
Chapter V. Summability of Series ff2[/] and ^[f, B]
by a Method of the Marcinkiewicz Type
5.1. Summability Almost Everywhere of Series r2[/] and ^[f, B]
by a Method of the Marcinkiewicz Type 243
5.2. Some Approximating Properties of Marcinkiewicz Type Means
of the Series a2[f] in the Spaces IP(T2), p € [1, +oo] 255
5.3. Unsolved Problems 266
Bibliography 267
Index 299
|
| any_adam_object | 1 |
| author | Žižiašvili, Levan 1934- |
| author_GND | (DE-588)104311355 |
| author_facet | Žižiašvili, Levan 1934- |
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| author_variant | l ž lž |
| building | Verbundindex |
| bvnumber | BV011041446 |
| classification_rvk | SK 450 |
| classification_tum | MAT 420f |
| ctrlnum | (OCoLC)832795930 (DE-599)BVBBV011041446 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011041446 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T14:21:12Z |
| institution | BVB |
| isbn | 0792340884 |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007393086 |
| oclc_num | 832795930 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-12 DE-29T DE-703 |
| owner_facet | DE-91G DE-BY-TUM DE-12 DE-29T DE-703 |
| physical | XII, 300 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spellingShingle | Žižiašvili, Levan 1934- Trigonometric Fourier series and their conjugates Mathematics and its applications Fourier-Reihe (DE-588)4155109-6 gnd |
| subject_GND | (DE-588)4155109-6 |
| title | Trigonometric Fourier series and their conjugates |
| title_auth | Trigonometric Fourier series and their conjugates |
| title_exact_search | Trigonometric Fourier series and their conjugates |
| title_full | Trigonometric Fourier series and their conjugates by Levan Zhizhiashvili |
| title_fullStr | Trigonometric Fourier series and their conjugates by Levan Zhizhiashvili |
| title_full_unstemmed | Trigonometric Fourier series and their conjugates by Levan Zhizhiashvili |
| title_short | Trigonometric Fourier series and their conjugates |
| title_sort | trigonometric fourier series and their conjugates |
| topic | Fourier-Reihe (DE-588)4155109-6 gnd |
| topic_facet | Fourier-Reihe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007393086&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT ziziasvililevan trigonometricfourierseriesandtheirconjugates |