Trigonometric Fourier series and their conjugates
Author(s)
Bibliographic Information
Trigonometric Fourier series and their conjugates
(Mathematics and its applications, v. 372)
Kluwer Academic Publishers, c1996
Available at 35 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Revised and updated translation of the Russian work
Includes bibliographical references and index
Description and Table of Contents
Description
Research in the theory of trigonometric series has been carried out for over two centuries. The results obtained have greatly influenced various fields of mathematics, mechanics, and physics. Nowadays, the theory of simple trigonometric series has been developed fully enough (we will only mention the monographs by Zygmund [15, 16] and Bari [2]). The achievements in the theory of multiple trigonometric series look rather modest as compared to those in the one-dimensional case though multiple trigonometric series seem to be a natural, interesting and promising object of investigation. We should say, however, that the past few decades have seen a more intensive development of the theory in this field. To form an idea about the theory of multiple trigonometric series, the reader can refer to the surveys by Shapiro [1], Zhizhiashvili [16], [46], Golubov [1], D'yachenko [3]. As to monographs on this topic, only that ofYanushauskas [1] is known to me. This book covers several aspects of the theory of multiple trigonometric Fourier series: the existence and properties of the conjugates and Hilbert transforms of integrable functions; convergence (pointwise and in the LP-norm, p > 0) of Fourier series and their conjugates, as well as their summability by the Cesaro (C,a), a> -1, and Abel-Poisson methods; approximating properties of Cesaro means of Fourier series and their conjugates.
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 Cesaro 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 Cesaro 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.
by "Nielsen BookData"