Walsh series and transforms: theory and applications
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Dordrecht u.a.
Kluwer
1991
|
| Schriftenreihe: | Mathematics and its applications / Soviet series
64. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Russ. übers. |
| Beschreibung: | XIII, 368 S. |
| ISBN: | 0792311000 |
Internformat
MARC
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| 100 | 1 | |a Golubov, Boris I. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Rjady i preobrazovanija uolša |
| 245 | 1 | 0 | |a Walsh series and transforms |b theory and applications |c by B. Golubov ; A. Efimov and V. Skvortsov |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer |c 1991 | |
| 300 | |a XIII, 368 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications / Soviet series |v 64. | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 4 | |a Décomposition (Mathématiques) | |
| 650 | 7 | |a Décomposition (Mathématiques) |2 ram | |
| 650 | 7 | |a Fonctions (Mathématiques) |2 ram | |
| 650 | 7 | |a Fourier-analyse |2 gtt | |
| 650 | 4 | |a Walsh, Fonctions de | |
| 650 | 7 | |a Walsh, fonctions de |2 ram | |
| 650 | 7 | |a approximation |2 inriac | |
| 650 | 7 | |a décomposition fonction |2 inriac | |
| 650 | 7 | |a fonction L |2 inriac | |
| 650 | 7 | |a fonction Walsh |2 inriac | |
| 650 | 7 | |a fonction multiplicative |2 inriac | |
| 650 | 7 | |a intégralité |2 inriac | |
| 650 | 7 | |a opérateur |2 inriac | |
| 650 | 7 | |a série Fourier |2 inriac | |
| 650 | 7 | |a série Walsh |2 inriac | |
| 650 | 7 | |a série Walsh-Fourier |2 inriac | |
| 650 | 7 | |a traitement image numérique |2 inriac | |
| 650 | 7 | |a transformée Walsh |2 inriac | |
| 650 | 4 | |a Decomposition (Mathematics) | |
| 650 | 4 | |a Walsh functions | |
| 650 | 0 | 7 | |a Walsh-Funktionensystem |0 (DE-588)4189028-0 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Efimov, Aleksandr V. |e Verfasser |4 aut | |
| 700 | 1 | |a Skvorcov, Valentin A. |e Verfasser |4 aut | |
| 810 | 2 | |a Soviet series |t Mathematics and its applications |v 64. |w (DE-604)BV004708148 |9 64 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-004211180 | ||
Datensatz im Suchindex
| _version_ | 1804120868103651328 |
|---|---|
| adam_text | TABLE OF CONTENTS
Series Editor s Preface v
Preface xj
Foreword xiii
Chapter 1
WALSH FUNCTIONS AND THEIR GENERALIZATIONS
§1.1 The Walsh functions on the interval [0,1) 1
§1.2 The Walsh system on the group 5
§1.3 Other definitions of the Walsh system. Its connection with the Haar system 14
§1.4 Walsh series. The Dirichlet kernel 18
§1.5 Multiplicative systems and their continual analogues 21
Chapter 2
WALSH FOURIER SERIES
BASIC PROPERTIES
§2.1 Elementary properties of Walsh Fourier series. Formulae for partial sums 35
§2.2 The Lebesgue constants 10
§2.3 Moduli of continuity of functions and uniform convergence of Walsh Fourier series 13
§2.4 Other tests for uniform convergence Al
§2.5 The localization principle. Tests for convergence of a Walsh Fourier series at a point ... 50
§2.6 The Walsh system as a complete, closed system 56
§2.7 Estimates of Walsh Fourier coefficients. Absolute convergence of Walsh Fourier series . .59
§2.8 Fourier series in multiplicative systems 66
Chapter 3
GENERAL WALSH SERIES AND FOURIER STIELTJES SERIES
QUESTIONS ON UNIQUENESS OF REPRESENTATION OF
FUNCTIONS BY WALSH SERIES
§3.1 General Walsh series as a generalized Stieltjes series 71
§3.2 Uniqueness theorems for representation of functions by pointwise convergent
Walsh series 80
§3.3 A localization theorem for general Walsh series 8(i
§3.4 Examples of null series in the Walsh system. The concept of (/ sets and .U .sets 89
viii TABLE OF CONTENTS
Chapter 4
SUMMATION OF WALSH SERIES BY
THE METHOD OF ARITHMETIC MEANS
§4.1 Linear methods of summation. Regularity of the arithmetic means 94
§4.2 The kernel for the method of arithmetic means for Walsh Fourier series 97
§4.3 Uniform (C, 1) summability of Walsh Fourier series of continuous functions 99
§4.4 (C, 1) summability of Fourier Stieltjes series 103
Chapter 5
OPERATORS IN THE THEORY OF WALSH FOURIER SERIES
§5.1 Some information from the theory of operators on spaces of measurable functions 112
§5.2 The Hardy Littlewood maximal operator corresponding to sequences of dyadic nets ... 117
§5.3 Partial sums of Walsh Fourier series as operators 119
§5.4 Convergence of Walsh Fourier series in Lp[0,1) 124
Chapter 6
GENERALIZED MULTIPLICATIVE TRANSFORMS
§6.1 Existence and properties of generalized multiplicative transforms 127
§6.2 Representation of functions in 1^(0, oo) by their multiplicative transforms 135
§6.3 Representation of functions in 1/(0, oo), 1 p 2, by their multiplicative transforms .147
Chapter 7
WALSH SERIES WITH MONOTONE DECREASING COEFFICIENTS
§7.1 Convergence and integrability 153
§7.2 Series with quasiconvex coefficients 163
§7.3 Fourier series of functions in Lp 166
Chapter 8
LACUNARY SUBSYSTEMS OF THE WALSH SYSTEM
§8.1 The Rademacher system 173
§8.2 Other lacunary subsystems 177
§8.3 The Central Limit Theorem for lacunary Walsh series 185
TABLE OF CONTENTS ix
Chapter 9
DIVERGENT WALSH FOURIER SERIES
ALMOST EVERYWHERE CONVERGENCE OF
WALSH FOURIER SERIES OF L2 FUNCTIONS
§9.1 Everywhere divergent Walsh Fourier series 194
§9.2 Almost everywhere convergence of Walsh Fourier series of L2[0,1) functions 198
Chapter 10
APPROXIMATIONS BY WALSH AND HAAR POLYNOMIALS
§10.1 Approximation in uniform norm 213
§10.2 Approximation in the Lp norm 219
§10.3 Connections between best approximations and integrability conditions 230
§10.4 Connections between best approximations and integrability conditions
(continued) 236
§10.5 Best approximations by means of multiplicative and step functions 255
Chapter 11
APPLICATIONS OF MULTIPLICATIVE SERIES
AND TRANSFORMS
TO DIGITAL INFORMATION PROCESSING
§11.1 Discrete multiplicative transforms 260
§11.2 Computation of the discrete multiplicative transform 270
§11.3 Applications of discrete multiplicative transforms to information compression 281
§11.4 Peculiarities of processing two dimensional numerical problems with discrete
multiplicative transforms 295
§11.5 A description of classes of discrete transforms which allow fast algorithms 298
Chapter 12
OTHER APPLICATIONS OF MULTIPLICATIVE FUNCTIONS
AND TRANSFORMS
§12.1 Construction of digital filters based on multiplicative transforms 310
§12.2 Multiplicative holographic transformations for image processing 313
§12.3 Solutions to certain optimization problems 323
x TABLE OF CONTENTS
APPENDICES
Appendix 1 Abelian groups 341
Appendix 2 Metric spaces. Metric groups 342
Appendix 3 Measure spaces 343
Appendix 4 Measurable functions. The Lebesgue integral 345
Appendix 5 Normed linear spaces. Hilbert spaces 350
Commentary 354
References 359
Index 365
|
| any_adam_object | 1 |
| author | Golubov, Boris I. Efimov, Aleksandr V. Skvorcov, Valentin A. |
| author_facet | Golubov, Boris I. Efimov, Aleksandr V. Skvorcov, Valentin A. |
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| dewey-ones | 515 - Analysis |
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| id | DE-604.BV006595157 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:48:55Z |
| institution | BVB |
| isbn | 0792311000 |
| language | English Russian |
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| physical | XIII, 368 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
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| publisher | Kluwer |
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| series2 | Mathematics and its applications / Soviet series |
| spelling | Golubov, Boris I. Verfasser aut Rjady i preobrazovanija uolša Walsh series and transforms theory and applications by B. Golubov ; A. Efimov and V. Skvortsov Dordrecht u.a. Kluwer 1991 XIII, 368 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Soviet series 64. Aus dem Russ. übers. Décomposition (Mathématiques) Décomposition (Mathématiques) ram Fonctions (Mathématiques) ram Fourier-analyse gtt Walsh, Fonctions de Walsh, fonctions de ram approximation inriac décomposition fonction inriac fonction L inriac fonction Walsh inriac fonction multiplicative inriac intégralité inriac opérateur inriac série Fourier inriac série Walsh inriac série Walsh-Fourier inriac traitement image numérique inriac transformée Walsh inriac Decomposition (Mathematics) Walsh functions Walsh-Funktionensystem (DE-588)4189028-0 gnd rswk-swf Walsh-Funktionensystem (DE-588)4189028-0 s DE-604 Efimov, Aleksandr V. Verfasser aut Skvorcov, Valentin A. Verfasser aut Soviet series Mathematics and its applications 64. (DE-604)BV004708148 64 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004211180&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Golubov, Boris I. Efimov, Aleksandr V. Skvorcov, Valentin A. Walsh series and transforms theory and applications Décomposition (Mathématiques) Décomposition (Mathématiques) ram Fonctions (Mathématiques) ram Fourier-analyse gtt Walsh, Fonctions de Walsh, fonctions de ram approximation inriac décomposition fonction inriac fonction L inriac fonction Walsh inriac fonction multiplicative inriac intégralité inriac opérateur inriac série Fourier inriac série Walsh inriac série Walsh-Fourier inriac traitement image numérique inriac transformée Walsh inriac Decomposition (Mathematics) Walsh functions Walsh-Funktionensystem (DE-588)4189028-0 gnd |
| subject_GND | (DE-588)4189028-0 |
| title | Walsh series and transforms theory and applications |
| title_alt | Rjady i preobrazovanija uolša |
| title_auth | Walsh series and transforms theory and applications |
| title_exact_search | Walsh series and transforms theory and applications |
| title_full | Walsh series and transforms theory and applications by B. Golubov ; A. Efimov and V. Skvortsov |
| title_fullStr | Walsh series and transforms theory and applications by B. Golubov ; A. Efimov and V. Skvortsov |
| title_full_unstemmed | Walsh series and transforms theory and applications by B. Golubov ; A. Efimov and V. Skvortsov |
| title_short | Walsh series and transforms |
| title_sort | walsh series and transforms theory and applications |
| title_sub | theory and applications |
| topic | Décomposition (Mathématiques) Décomposition (Mathématiques) ram Fonctions (Mathématiques) ram Fourier-analyse gtt Walsh, Fonctions de Walsh, fonctions de ram approximation inriac décomposition fonction inriac fonction L inriac fonction Walsh inriac fonction multiplicative inriac intégralité inriac opérateur inriac série Fourier inriac série Walsh inriac série Walsh-Fourier inriac traitement image numérique inriac transformée Walsh inriac Decomposition (Mathematics) Walsh functions Walsh-Funktionensystem (DE-588)4189028-0 gnd |
| topic_facet | Décomposition (Mathématiques) Fonctions (Mathématiques) Fourier-analyse Walsh, Fonctions de Walsh, fonctions de approximation décomposition fonction fonction L fonction Walsh fonction multiplicative intégralité opérateur série Fourier série Walsh série Walsh-Fourier traitement image numérique transformée Walsh Decomposition (Mathematics) Walsh functions Walsh-Funktionensystem |
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