Lebesgue Points and Summability of Higher Dimensional Fourier Series

Ferenc Weisz

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English

Springer Nature Switzerland AG
13 June 2021

Functional analysis & transforms; Integral calculus & equations

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.

By: Ferenc Weisz
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: 2021 ed.
Dimensions: Height: 235mm, Width: 155mm,
Weight: 623g
ISBN: 9783030746353
ISBN 10: 3030746356
Pages: 290
Publication Date: 13 June 2021
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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

Reviews for Lebesgue Points and Summability of Higher Dimensional Fourier Series

The book is mainly based on the very many interesting author's results published in the last 20-30 years. It will be useful for ... graduate, postgraduate and Ph.D. students. (Sorin Gheorghe Gal, zbMATH 1475.42017, 2022)