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Functions of bounded variation and t...

Liflyand, Elijah.

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Functions of bounded variation and their Fourier transforms

Record Type:	Electronic resources : Monograph/item
Title/Author:	Functions of bounded variation and their Fourier transforms/ by Elijah Liflyand.
Author:	Liflyand, Elijah.
Published:	Cham :Springer International Publishing : : 2019.,
Description:	xxiv, 194 p. :ill., digital ;24 cm.
[NT 15003449]:	Stock and tools -- Functions with derivative in a Hardy space -- Integrability spaces: wide, wider and widest -- Sharper results -- Stock and tools for several dimensions -- Integrability of the Fourier transforms -- Sharp results -- Bounded variation and discretization -- Multidimensional case: radial functions.
Contained By:	Springer eBooks
Subject:	Functions of bounded variation. -
Online resource:	https://doi.org/10.1007/978-3-030-04429-9
ISBN:	9783030044299

Functions of bounded variation and their Fourier transforms
Liflyand, Elijah.

Functions of bounded variation and their Fourier transforms[electronic resource] /by Elijah Liflyand. - Cham :Springer International Publishing :2019. - xxiv, 194 p. :ill., digital ;24 cm. - Applied and numerical harmonic analysis,2296-5009. - Applied and numerical harmonic analysis..

Stock and tools -- Functions with derivative in a Hardy space -- Integrability spaces: wide, wider and widest -- Sharper results -- Stock and tools for several dimensions -- Integrability of the Fourier transforms -- Sharp results -- Bounded variation and discretization -- Multidimensional case: radial functions.

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.

ISBN: 9783030044299

Standard No.: 10.1007/978-3-030-04429-9doiSubjects--Topical Terms:

705270
Functions of bounded variation.

LC Class. No.: QA331.5

Dewey Class. No.: 515.8

Functions of bounded variation and their Fourier transforms
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100 1 $a Liflyand, Elijah. $3 2108864
245 1 0 $a Functions of bounded variation and their Fourier transforms $h [electronic resource] / $c by Elijah Liflyand.
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300 $a xxiv, 194 p. : $b ill., digital ; $c 24 cm.
490 1 $a Applied and numerical harmonic analysis, $x 2296-5009
505 0 $a Stock and tools -- Functions with derivative in a Hardy space -- Integrability spaces: wide, wider and widest -- Sharper results -- Stock and tools for several dimensions -- Integrability of the Fourier transforms -- Sharp results -- Bounded variation and discretization -- Multidimensional case: radial functions.
520 $a 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.
650 0 $a Functions of bounded variation. $3 705270
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