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Functions of Bounded Variation and Their Fourier Transforms

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Functions of Bounded Variation and Their Fourier Transforms/ by Elijah Liflyand.
作者:	Liflyand, Elijah.
面頁冊數:	XXIV, 194 p.online resource. :
Contained By:	Springer Nature eBook
標題:	Harmonic analysis. -
電子資源:	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. - 1st ed. 2019. - XXIV, 194 p.online resource. - 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:

672073
Harmonic analysis.

LC Class. No.: QA403-403.3

Dewey Class. No.: 515.785

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