Functions of Bounded Variation and Their F...

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Beschreibung

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.

Zusammenfassung

Covers almost all the aspects of the behavior of the Fourier transforms of functions of bounded variation

Many known and new spaces are considered

A must to read for those who are interested in function spaces and their interrelations

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2019
Fachbereich:	Analysis
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xxiv 194 S.
ISBN-13:	9783030044282
ISBN-10:	3030044289
Sprache:	Englisch
Herstellernummer:	978-3-030-04428-2
Einband:	Gebunden
Autor:	Liflyand, Elijah
Auflage:	1st edition 2019
Hersteller:	Springer International Publishing
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	241 x 160 x 19 mm
Von/Mit:	Elijah Liflyand
Erscheinungsdatum:	21.03.2019
Gewicht:	0,524 kg