Fourier analysis and approximation of functions /
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 i...
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| Format: | eBook |
| Language: | English |
| Published: |
Dordrecht ; London :
Springer Science+Business Media,
2004.
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | 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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| Item Description: | Originally published: Dordrecht; London: Kluwer Academic Publishers, 2004. "Softcover reprint of the hardcover 1st edition 2004"--Title page verso. |
| Physical Description: | 1 online resource (xiii, 585 pages) |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9781402023422 (electronic bk.) 1402023421 (electronic bk.) 9781402028762 (electronic bk.) 1402028768 (electronic bk.) |