Overview
- 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
Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)
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Table of contents (9 chapters)
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Front Matter
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One-dimensional Case
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Front Matter
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Multi-dimensional Case
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Functions of Bounded Variation and Their Fourier Transforms
Authors: Elijah Liflyand
Series Title: Applied and Numerical Harmonic Analysis
DOI: https://doi.org/10.1007/978-3-030-04429-9
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-04428-2Published: 21 March 2019
eBook ISBN: 978-3-030-04429-9Published: 06 March 2019
Series ISSN: 2296-5009
Series E-ISSN: 2296-5017
Edition Number: 1
Number of Pages: XXIV, 194
Topics: Abstract Harmonic Analysis