Lebesgue points and summability of higher dimensional Fourier series / Ferenc Weisz.
Weisz, Ferenc, 1964- author.
2021
QA404 .W45 2021
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Title Lebesgue points and summability of higher dimensional Fourier series / Ferenc Weisz.
Author Weisz, Ferenc, 1964- author.
ISBN 9783030746360 (electronic bk.)
3030746364 (electronic bk.)
9783030746353
3030746356
DOI https://doi.org/10.1007/978-3-030-74636-0
Published Cham : Birkhäuser, [2021]
Copyright ©2021
Language English
Description 1 online resource (xiii, 290 pages) : illustrations (black and white and color)
Other Standard Identifiers 10.1007/978-3-030-74636-0 doi
Call Number QA404 .W45 2021
Dewey Decimal Classification 515/.2433
Summary This monograph presents the summability of higher dimensional Fourier series, and generalizes the concept of Lebesgue points. Focusing on Fejér and Cesàro summability, as well as theta-summation, readers will become more familiar with a wide variety of summability methods. Within the theory of higher dimensional summability of Fourier series, the book also provides a much-needed simple proof of Lebesgue's theorem, filling a gap in the literature. Recent results and real-world applications are highlighted as well, making this a timely resource. The book is structured into four chapters, prioritizing clarity throughout. Chapter One covers basic results from the one-dimensional Fourier series, and offers a clear proof of the Lebesgue theorem. In Chapter Two, convergence and boundedness results for the lq-summability are presented. The restricted and unrestricted rectangular summability are provided in Chapter Three, as well as the sufficient and necessary condition for the norm convergence of the rectangular theta-means. Chapter Four then introduces six types of Lebesgue points for higher dimensional functions. Lebesgue Points and Summability of Higher Dimensional Fourier Series will appeal to researchers working in mathematical analysis, particularly those interested in Fourier and harmonic analysis. Researchers in applied fields will also find this useful.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Available in Other Form Print version: 9783030746353
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One-dimensional Fourier series
lq-summability of higher dimensional Fourier series
Rectangular summability of higher dimensional Fourier series
Lebesgue points of higher dimensional functions.

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