Trigonometric Fourier Series and Their Conjugates

Trigonometric Fourier Series and Their Conjugates

by L. Zhizhiashvili

Paperback(Softcover reprint of the original 1st ed. 1996)

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Overview

Trigonometric Fourier Series and Their Conjugates by L. Zhizhiashvili

This book presents in a coherent way the results obtained in the following aspects of the theory of multiple trigonometric Fourier series: the existence and properties of the conjugates and Hilbert transforms of integrable functions of several variables; convergence of Fourier series and their conjugates, as well as their summability by Cesàro and Abel-Poisson methods; and approximating properties of Cesàro means of Fourier series and their conjugates.
Special emphasis is put on new effects which arise from dealing with multiple series and which are not inherent in the one-dimensional case. Unsolved problems are formulated separately.
Audience: This volume will prove useful to both graduate students and research workers in the field of Fourier analysis, approximations and expansions, integral transforms, and operational calculus.

Product Details

ISBN-13: 9789401066129
Publisher: Springer Netherlands
Publication date: 10/12/2011
Series: Mathematics and Its Applications Series , #372
Edition description: Softcover reprint of the original 1st ed. 1996
Pages: 308
Product dimensions: 6.30(w) x 9.45(h) x 0.03(d)

Table of Contents

Preface. Part 1: Simple Trigonometric Series. I. The Conjugation Operator and the Hilbert Transform. II. Pointwise Convergence and Summability of Trigonometric Series. III. Convergence and Summability of Trigonometric Fourier Series and Their Conjugates in the Spaces Lp(T), p epsilon]0,+INFINITY[. IV. Some Approximating Properties of Cesàro Means of the Series sigma[f] and sigma-bar[f]. Part 2: Multiple Trigonometric Series. I. Conjugate Functions and Hilbert Transforms of Functions of Several Variables. II. Convergence and Summability at a Point or Almost Everywhere of Multiple Trigonometric Fourier Series and Their Conjugates. III. Some Approximating Properties of n-Fold Cesàro Means of the Series sigman[f] and sigma-barn[f,B]. IV. Convergence and Summability of Multiple Trigonometric Fourier Series and Their Conjugates in the Spaces Lp(Tn), p epsilon]0,+INFINITY]. V. Summability of Series sigma2[f] and sigma-bar2[f,B]. Bibliography. Index.

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