Fourier Analysis and Approximation of Functions

Released on by Roald M. Trigub
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  • Fourier Analysis and Approximation of Functions Book Detail

  • Author : Roald M. Trigub
  • Release Date : 2012-11-07
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 595
  • ISBN 13 : 1402028768
  • File Size : 46,46 MB
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Fourier Analysis and Approximation of Functions by Roald M. Trigub PDF Summary

Book 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.

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