Fourier Analysis and Approximation of Functions

Authors: Trigub, Roald M., Belinsky, Eduard S.

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Softcover 103,99 €
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About this book

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.

Reviews

From the reviews:

"The motivation for writing this extensive monograph of over 500 pages is to compile the basic and more current results in Fourier analysis that are particularly useful for solving certain approximation problems. … This is a very well written monograph with very rich content. It is an excellent reference source for researchers in approximation theory, and is also suitable for adoption as textbook for a graduate course … ." (Charles K. Chui, Mathematical Reviews, Issue 2005 k)

“Part of the book is classical approximation theory and classical Fourier analysis (series and integrals in one and more variables) with the emphasis on approximation theory. … each chapter is concluded by a rather extensive section ‘Further problems and theorems’ which introduces extended or related results as exercises, often suggesting methods for the solutions, and a guide to the literature. … When used as a textbook, it will be a … source of inspiration for a researcher in approximation theory or harmonic analysis.” (Adhemar Bultheel, Bulletin of the Belgian Mathematical Society, Vol. 15 (1), 2008)


Table of contents (11 chapters)

  • Representation Theorems

    Trigub, Roald M. (et al.)

    Pages 1-24

    Preview Buy Chapter 30,19 €
  • Fourier Series

    Trigub, Roald M. (et al.)

    Pages 25-66

    Preview Buy Chapter 30,19 €
  • Fourier Integral

    Trigub, Roald M. (et al.)

    Pages 67-104

    Preview Buy Chapter 30,19 €
  • Discretization. Direct and Inverse Theorems of Approximation Theory

    Trigub, Roald M. (et al.)

    Pages 105-199

    Preview Buy Chapter 30,19 €
  • Extremal Problems of Approximation Theory

    Trigub, Roald M. (et al.)

    Pages 201-254

    Preview Buy Chapter 30,19 €

Buy this book

eBook 83,29 €
price for Spain (gross)
  • ISBN 978-1-4020-2876-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 103,99 €
price for Spain (gross)
  • ISBN 978-1-4020-2341-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 103,99 €
price for Spain (gross)
  • ISBN 978-90-481-6641-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Fourier Analysis and Approximation of Functions
Authors
Copyright
2004
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-1-4020-2876-2
DOI
10.1007/978-1-4020-2876-2
Hardcover ISBN
978-1-4020-2341-5
Softcover ISBN
978-90-481-6641-1
Edition Number
1
Number of Pages
XIV, 586
Topics