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Lebesgue points and summability of higher dimensional Fourier series

Record Type:	Electronic resources : Monograph/item
Title/Author:	Lebesgue points and summability of higher dimensional Fourier seriesby Ferenc Weisz.
Author:	Weisz, Ferenc.
Published:	Cham :Springer International Publishing :2021.
Description:	xiii, 290 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Fourier series.
Online resource:	https://doi.org/10.1007/978-3-030-74636-0
ISBN:	9783030746360$q(electronic bk.)

Lebesgue points and summability of higher dimensional Fourier series
Weisz, Ferenc.

Lebesgue points and summability of higher dimensional Fourier series[electronic resource] /by Ferenc Weisz. - Cham :Springer International Publishing :2021. - xiii, 290 p. :ill. (some col.), digital ;24 cm.

One-dimensional Fourier series -- lq-summability of higher dimensional Fourier series -- Rectangular summability of higher dimensional Fourier series -- Lebesgue points of higher dimensional functions.

This monograph presents the summability of higher dimensional Fourier series, and generalizes the concept of Lebesgue points. Focusing on Fejer and Cesaro 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.

ISBN: 9783030746360$q(electronic bk.)

Standard No.: 10.1007/978-3-030-74636-0doiSubjects--Topical Terms:

218948
Fourier series.

LC Class. No.: QA404 / .W457 2021

Dewey Class. No.: 515.2433

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505 0 $a One-dimensional Fourier series -- lq-summability of higher dimensional Fourier series -- Rectangular summability of higher dimensional Fourier series -- Lebesgue points of higher dimensional functions.
520 $a This monograph presents the summability of higher dimensional Fourier series, and generalizes the concept of Lebesgue points. Focusing on Fejer and Cesaro 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.
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