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Fourier Analysis and Approximation of Functions [electronic resource] /
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.
| Main Authors: | , , |
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| Format: | Texto biblioteca |
| Language: | eng |
| Published: |
Dordrecht : Springer Netherlands : Imprint: Springer,
2004
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| Subjects: | Mathematics., Approximation theory., Fourier analysis., Functional analysis., Measure theory., Sequences (Mathematics)., Approximations and Expansions., Fourier Analysis., Sequences, Series, Summability., Measure and Integration., Functional Analysis., |
| Online Access: | http://dx.doi.org/10.1007/978-1-4020-2876-2 |
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