Fourier Transforms and Approximations

by A M Sedletskii

Overview

Three classes of Fourier transforms are presented: Fourier (Laplace) transforms on the halfline, Fourier transforms of measures with compact support and Fourier transforms of rapidly decreasing functions (on whole line). The focus is on the behaviour of Fourier transforms in the region of analyticity and the distribution of their zeros. Applications of results are presented: approximation by exponentials on the finite interval; behavior of the nonharmonic Fourier series; Müntz-Szasz's problem of approximation by powers on unit interval; approximation by weighted exponentials on whole line.

Product Details

ISBN-13:	9789056992347
Publisher:	Taylor & Francis
Publication date:	09/20/2000
Series:	Analytical Methods and Special Functions
Pages:	272
Product dimensions:	7.00(w) x 10.00(h) x (d)

Table of Contents

1. Auxiliary Informations from the Analysis 2. Distribution of Zeros of Finite Fourier Transforms 3. Estimates of Fourier and Laplace Transforms and Their Applications 4. Stability of Classes of Finite Fourier Transforms 5. Laplace Transforms in the Weighted Spaces Lp and Its Applications 6. Nonharmonic Fourier Series 7. Muntz-Szasz's Problem 8. Fourier Transforms of Rapidly Decreasing Functions 9. Approximate Properties of Systems of Exponents in the Lebesgue's Spaces on All Line

Editorial Reviews

Sedletskii (mathematical analysis, Moscow State U.) says a more detailed title would be Fourier transforms that are analytic functions and their applications to the function approximation by means of exponents and powers on subsets of the real axis: on an interval, on a semi-axis, and on the whole axis. But that would have left no room for his name on the cover. He considers the three classes of Fourier transforms: finite, on a semi-axis, and of rapidly decreasing function on the whole line. As well as synthesizing what is currently known about the topics, he presents some unsolved problems. A translator is identified, but no Russian edition. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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