Fourier transforms and approximations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
Gordon and Breach Science Publ.
2000
|
| Series: | Analytical methods and special functions
4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 261 S. |
| ISBN: | 9056992341 9789056992347 |
Staff View
MARC
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Record in the Search Index
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| adam_text | FOURIER TRANSFORMS AND APPROXIMATIONS A.M. SEDLETSKII MOSCOW STATE
UNIVERSITY, RUSSIA TRANSLATED FROM THE RUSSIAN BY E.V. PANKRATIEV GORDON
AND BREACH SCIENCE PUBLISHERS AUSTRALIA * CANADA * FRANCE * GERMANY *
INDIA * JAPAN * LUXEMBOURG MALAYSIA * THE NETHERLANDS * RUSSIA *
SINGAPORE * SWITZERLAND CONTENTS PREFACE VII CHAPTER 1. NOTATION AND
SOME PRELIMINARIES FROM ANALYSIS 1 1.1. GENERAL NOTATION 1 1.2. SLOWLY
VARYING FUNCTIONS 2 1.3. SYSTEMS IN BANACH SPACES 4 1.4. INTERPOLATION
OF LINEAR OPERATORS 5 1.5. FOURIER TRANSFORMS 6 1.6. HARDY SPACES IF 7
1.7. ENTIRE FUNCTIONS 8 COMMENTS TO CHAPTER 1 10 CHAPTER 2. DISTRIBUTION
OF ZEROS OF FINITE FOURIER (LAPLACE) TRANSFORMS 11 2.1. ON ZEROS OF
FINITE LAPLACE TRANSFORMS 11 2.2. ON ZEROS OF FOURIER SINE- AND
COSINE-TRANSFORMS 16 2.3. BOUNDS FOR ZEROS OF THE FINITE LAPLACE
TRANSFORMS 25 2.4. A CONDITION FOR ALL THE ZEROS OF AN ENTIRE FUNCTION
OF EXPONENTIAL TYPE TO LIE IN A CURVILINEAR HALF-PLANE 31 COMMENTS AND
SUPPLEMENTS TO CHAPTER 2 39 CHAPTER 3. ESTIMATES OF FOURIER AND LAPLACE
TRANSFORMS AND THEIR APPLICATIONS 41 3.1. ASYMPTOTIC BEHAVIOUR OF FINITE
LAPLACE TRANSFORMS 41 3.2. COMPLEX VARIANTS OF THE ABELIAN THEOREM FOR
LAPLACE TRANSFORMS 52 3.3. DECREASING FINITE FOURIER TRANSFORMS AND
THEIR APPLICATION TO THE APPROXIMATION 55 3.4. FINITE FOURIER TRANSFORMS
WITHOUT ZEROS IN A NEIGHBOURHOOD OF THE REAL AXIS 60 COMMENTS AND
SUPPLEMENTS TO CHAPTER 3 63 CHAPTER 4. LAPLACE TRANSFORMS IN THE WEIGHT
SPACES IP AND THEIR APPLICATIONS 65 4.1. LAPLACE TRANSFORMS AS OPERATORS
IN THE SPACES LP A 65 4.2. ON COMPLETENESS AND NON-MINIMALITY OF A
SYSTEM OF EXPONENTS IN LP(- N, IT) 69 COMMENTS AND SUPPLEMENTS TO
CHAPTER 4 81 CHAPTER 5. STABILITY OF CLASSES OF FINITE FOURIER
TRANSFORMS AND ITS APPLICATION . 83 5.1. THE INVARIANCE OF THE CLASS J L
2 83 5.2. THE INVARIANCE OF THE CLASS J I? 95 5.3. ENTIRE FUNCTIONS OF
BERNSTEIN S CLASS THAT ARE NOT FOURIER-STIELTJES TRANSFORMS 101 5.4.
EXCESSES OF SYSTEMS OF EXPONENTS 111 COMMENTS AND SUPPLEMENTS TO CHAPTER
5 119 VI CONTENTS CHAPTER 6. NON-HARMONIC FOURIER SERIES (BEHAVIOUR ON
THE INITIAL INTERVAL) 121 6.1. FORMULAE FOR PARTIAL SUMS 121 6.2.
NON-HARMONIC FOURIER SERIES AND THE CONDITION (A) 127 6.3.
EQUICONVERGENCE AND UNIFORM CONVERGENCE OF NON-HARMONIC FOURIER SERIES
137 COMMENTS AND SUPPLEMENTS TO CHAPTER 6 147 CHAPTER 7. NON-HARMONIC
FOURIER SERIES (BEHAVIOUR ON THE REAL LINE) 149 7.1. EXTENSION OF
CONVERGENCE OF QUASI-POLYNOMIALS 149 7.2. CONTINUATION OF FUNCTIONS FROM
THE INITIAL SEGMENT 161 7.3. CONVERGENCE AND SUMMABILITY OF NON-HARMONIC
FOURIER SERIES IN THE IF -NORM (1 P O) ON EVERY SEGMENT 164 7.4.
PROPERTIES OF THE SYSTEM (EXP(I(N + FT SGN N)T)) 171 COMMENTS AND
SUPPLEMENTS TO CHAPTER 7 176 CHAPTER 8. THE MIINTZ-SZASZ PROBLEM 179
8.1. THE CASE OF REAL EXPONENTS AND ANALYSIS OF THE PROBLEM IN THE
SPACES C AND IF, P 2 179 8.2. ON ZEROS OF ANALYTIC FUNCTIONS IN A DISK
187 8.3. ANALYSIS OF THE PROBLEM IN THE WEIGHT SPACES IF 194 COMMENTS
AND SUPPLEMENTS TO CHAPTER 8 210 CHAPTER 9. FOURIER TRANSFORMS OF
RAPIDLY DECREASING FUNCTIONS 211 9.1. THEOREMS OF PITT S TYPE 211 9.2.
FOURIER TRANSFORMS OF RAPIDLY DECREASING FUNCTIONS ON A HALF-LINE AND ON
THE LINE 218 COMMENTS AND SUPPLEMENTS TO CHAPTER 9 229 CHAPTER 10.
APPROXIMATION BY TRANSLATES AND EXPONENTS ON THE LINE 231 10.1. DENSE
FAMILIES OF TRANSLATES OF A FUNCTION ON A LINE 231 10.2. APPROXIMATIVE
PROPERTIES OF WEIGHTED EXPONENTS ON THE WHOLE LINE 245 COMMENTS AND
SUPPLEMENTS TO CHAPTER 10 254 REFERENCES 255 INDEX 261
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:47:29Z |
| institution | BVB |
| isbn | 9056992341 9789056992347 |
| language | English |
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| physical | X, 261 S. |
| publishDate | 2000 |
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| publisher | Gordon and Breach Science Publ. |
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| series | Analytical methods and special functions |
| series2 | Analytical methods and special functions |
| spelling | Sedletskij, A. M. Verfasser aut Fourier transforms and approximations A. M. Sedletskii Amsterdam Gordon and Breach Science Publ. 2000 X, 261 S. txt rdacontent n rdamedia nc rdacarrier Analytical methods and special functions 4 Fourier analysis Fourier transformations Fourier-Transformation (DE-588)4018014-1 gnd rswk-swf Fourier-Transformation (DE-588)4018014-1 s DE-604 Analytical methods and special functions 4 (DE-604)BV011932737 4 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009238026&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sedletskij, A. M. Fourier transforms and approximations Analytical methods and special functions Fourier analysis Fourier transformations Fourier-Transformation (DE-588)4018014-1 gnd |
| subject_GND | (DE-588)4018014-1 |
| title | Fourier transforms and approximations |
| title_auth | Fourier transforms and approximations |
| title_exact_search | Fourier transforms and approximations |
| title_full | Fourier transforms and approximations A. M. Sedletskii |
| title_fullStr | Fourier transforms and approximations A. M. Sedletskii |
| title_full_unstemmed | Fourier transforms and approximations A. M. Sedletskii |
| title_short | Fourier transforms and approximations |
| title_sort | fourier transforms and approximations |
| topic | Fourier analysis Fourier transformations Fourier-Transformation (DE-588)4018014-1 gnd |
| topic_facet | Fourier analysis Fourier transformations Fourier-Transformation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009238026&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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