Fourier Analysis and Approximation of Functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
2004
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | In Fourier Analysis and Approximation of Functions basics of classical Fourier Analysis are given as well as those of approximation by polynomials, splines and entire functions of exponential type. In Chapter 1 which has an introductory nature, theorems on convergence, in that or another sense, of integral operators are given. In Chapter 2 basic properties of simple and multiple Fourier series are discussed, while in Chapter 3 those of Fourier integrals are studied. The first three chapters as well as partially Chapter 4 and classical Wiener, Bochner, Bernstein, Khintchin, and Beurling theorems in Chapter 6 might be interesting and available to all familiar with fundamentals of integration theory and elements of Complex Analysis and Operator Theory. Applied mathematicians interested in harmonic analysis and/or numerical methods based on ideas of Approximation Theory are among them. In Chapters 6-11 very recent results are sometimes given in certain directions. Many of these results have never appeared as a book or certain consistent part of a book and can be found only in periodics; looking for them in numerous journals might be quite onerous, thus this book may work as a reference source. The methods used in the book are those of classical analysis, Fourier Analysis in finite-dimensional Euclidean space Diophantine Analysis, and random choice |
| Physical Description: | 1 Online-Ressource (XIV, 586 p) |
| ISBN: | 9781402028762 9789048166411 |
| DOI: | 10.1007/978-1-4020-2876-2 |
Staff View
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| 500 | |a In Fourier Analysis and Approximation of Functions basics of classical Fourier Analysis are given as well as those of approximation by polynomials, splines and entire functions of exponential type. In Chapter 1 which has an introductory nature, theorems on convergence, in that or another sense, of integral operators are given. In Chapter 2 basic properties of simple and multiple Fourier series are discussed, while in Chapter 3 those of Fourier integrals are studied. The first three chapters as well as partially Chapter 4 and classical Wiener, Bochner, Bernstein, Khintchin, and Beurling theorems in Chapter 6 might be interesting and available to all familiar with fundamentals of integration theory and elements of Complex Analysis and Operator Theory. Applied mathematicians interested in harmonic analysis and/or numerical methods based on ideas of Approximation Theory are among them. In Chapters 6-11 very recent results are sometimes given in certain directions. Many of these results have never appeared as a book or certain consistent part of a book and can be found only in periodics; looking for them in numerous journals might be quite onerous, thus this book may work as a reference source. The methods used in the book are those of classical analysis, Fourier Analysis in finite-dimensional Euclidean space Diophantine Analysis, and random choice | ||
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| isbn | 9781402028762 9789048166411 |
| language | English |
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| spelling | Trigub, Roald M. Verfasser aut Fourier Analysis and Approximation of Functions by Roald M. Trigub, Eduard S. Bellinsky Dordrecht Springer Netherlands 2004 1 Online-Ressource (XIV, 586 p) txt rdacontent c rdamedia cr rdacarrier In Fourier Analysis and Approximation of Functions basics of classical Fourier Analysis are given as well as those of approximation by polynomials, splines and entire functions of exponential type. In Chapter 1 which has an introductory nature, theorems on convergence, in that or another sense, of integral operators are given. In Chapter 2 basic properties of simple and multiple Fourier series are discussed, while in Chapter 3 those of Fourier integrals are studied. The first three chapters as well as partially Chapter 4 and classical Wiener, Bochner, Bernstein, Khintchin, and Beurling theorems in Chapter 6 might be interesting and available to all familiar with fundamentals of integration theory and elements of Complex Analysis and Operator Theory. Applied mathematicians interested in harmonic analysis and/or numerical methods based on ideas of Approximation Theory are among them. In Chapters 6-11 very recent results are sometimes given in certain directions. Many of these results have never appeared as a book or certain consistent part of a book and can be found only in periodics; looking for them in numerous journals might be quite onerous, thus this book may work as a reference source. The methods used in the book are those of classical analysis, Fourier Analysis in finite-dimensional Euclidean space Diophantine Analysis, and random choice Mathematics Fourier analysis Functional analysis Sequences (Mathematics) Approximations and Expansions Fourier Analysis Sequences, Series, Summability Measure and Integration Functional Analysis Mathematik Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s Approximation (DE-588)4002498-2 s 1\p DE-604 Approximationstheorie (DE-588)4120913-8 s 2\p DE-604 Bellinsky, Eduard S. Sonstige oth https://doi.org/10.1007/978-1-4020-2876-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Trigub, Roald M. Fourier Analysis and Approximation of Functions Mathematics Fourier analysis Functional analysis Sequences (Mathematics) Approximations and Expansions Fourier Analysis Sequences, Series, Summability Measure and Integration Functional Analysis Mathematik Approximationstheorie (DE-588)4120913-8 gnd Harmonische Analyse (DE-588)4023453-8 gnd Approximation (DE-588)4002498-2 gnd |
| subject_GND | (DE-588)4120913-8 (DE-588)4023453-8 (DE-588)4002498-2 |
| title | Fourier Analysis and Approximation of Functions |
| title_auth | Fourier Analysis and Approximation of Functions |
| title_exact_search | Fourier Analysis and Approximation of Functions |
| title_full | Fourier Analysis and Approximation of Functions by Roald M. Trigub, Eduard S. Bellinsky |
| title_fullStr | Fourier Analysis and Approximation of Functions by Roald M. Trigub, Eduard S. Bellinsky |
| title_full_unstemmed | Fourier Analysis and Approximation of Functions by Roald M. Trigub, Eduard S. Bellinsky |
| title_short | Fourier Analysis and Approximation of Functions |
| title_sort | fourier analysis and approximation of functions |
| topic | Mathematics Fourier analysis Functional analysis Sequences (Mathematics) Approximations and Expansions Fourier Analysis Sequences, Series, Summability Measure and Integration Functional Analysis Mathematik Approximationstheorie (DE-588)4120913-8 gnd Harmonische Analyse (DE-588)4023453-8 gnd Approximation (DE-588)4002498-2 gnd |
| topic_facet | Mathematics Fourier analysis Functional analysis Sequences (Mathematics) Approximations and Expansions Fourier Analysis Sequences, Series, Summability Measure and Integration Functional Analysis Mathematik Approximationstheorie Harmonische Analyse Approximation |
| url | https://doi.org/10.1007/978-1-4020-2876-2 |
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