(EBOOK PDF) Uniform Approximations by Trigonometric Polynomials 1st Edition by Alexander Stepanets ISBN 3110460777 9783110460773 full chapters

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Product details:

ISBN 10: 3110460777

ISBN 13: 978-3110460773

Author:  Alexander I. Stepanets 

Uniform Approximations by Trigonometric Polynomials 1st Edition: The theory of approximation of functions is one of the central branches in mathematical analysis and has been developed over a number of decades. This monograph deals with a series of problems related to one of the directions of the theory, namely, the approximation of periodic functions by trigonometric polynomials generated by linear methods of summation of Fourier series. More specific, the following linear methods are investigated: classical methods of Fourier, Fejir, Riesz, and Roginski. For these methods the so-called Kolmogorov-Nikol’skii problem is considered, which consists of finding exact and asymptotically exact qualities for the upper bounds of deviations of polynomials generated by given linear methods on given classes of 2?-periodic functions. Much attention is also given to the multidimensional case.
The material presented in this monograph did not lose its importance since the publication of the Russian edition (1981). Moreover, new material has been added and several corrections were made. In this field of mathematics numerous deep results were obtained, many important and complicated problems were solved, and new methods were developed, which can be extremely useful for many mathematicians. All principle problems considered in this monograph are given in the final form, i.e. in the form of exact asymptotic equalities, and, therefore, retain their importance and interest for a long time.

 

Uniform Approximations by Trigonometric Polynomials 1st Edition Table of contents:

Chapter 1. SIMPLEST EXTREMAL PROBLEMS
Chapter 2. APPROXIMATION OF FUNCTIONS OF ONE VARIABLE BY FOURIER SUMS
Chapter 3. APPROXIMATION OF FUNCTIONS OF MANY VARIABLES BY FOURIER SUMS
Chapter 4. FEJER SUMS
Chapter 5. SPHERICAL RIESZ SUMS
Chapter 6. ROGOSINSKI SUMS
Chapter 7. FAVARD SUMS

 

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Alexander Stepanets,Uniform,Approximations,Trigonometric,Polynomials