Functions of Bounded Variation and Their Fourier Transforms (Hardcover)

Elijah Liflyand

ISBN 10: 3030044289 / ISBN 13: 9783030044282

Published by Springer Nature Switzerland AG, Cham, 2019

About this Item

Hardcover. Functions of bounded variation represent an important class of functions. Studying their Fourier transforms is a valuable means of revealing their analytic properties. Moreover, it brings to light new interrelations between these functions and the real Hardy space and, correspondingly, between the Fourier transform and the Hilbert transform. This book is divided into two major parts, the first of which addresses several aspects of the behavior of the Fourier transform of a function of bounded variation in dimension one. In turn, the second part examines the Fourier transforms of multivariate functions with bounded Hardy variation. The results obtained are subsequently applicable to problems in approximation theory, summability of the Fourier series and integrability of trigonometric series. Moreover, it brings to light new interrelations between these functions and the real Hardy space and, correspondingly, between the Fourier transform and the Hilbert transform. In turn, the second part examines the Fourier transforms of multivariate functions with bounded Hardy variation. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

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Bibliographic Details

• Title: Functions of Bounded Variation and Their Fourier Transforms (Hardcover)
• Publisher: Springer Nature Switzerland AG, Cham
• Publication Date: 2019
• Language: English
• ISBN 10: 3030044289
• ISBN 13: 9783030044282
• Binding: Hardcover
• Condition: new

About this title

Synopsis

Functions of bounded variation represent an important class of functions. Studying their Fourier transforms is a valuable means of revealing their analytic properties. Moreover, it brings to light new interrelations between these functions and the real Hardy space and, correspondingly, between the Fourier transform and the Hilbert transform.  

This book is divided into two major parts, the first of which addresses several aspects of the behavior of the Fourier transform of a function of bounded variation in dimension one. In turn, the second part examines the Fourier transforms of multivariate functions with bounded Hardy variation. The results obtained are subsequently applicable to problems in approximation theory, summability of the Fourier series and integrability of trigonometric series.