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portada Lebesgue Points and Summability of Higher Dimensional Fourier Series
Type
Physical Book
Author
Publisher
Language
English
Pages
290
Format
Paperback
Dimensions
23.4 x 15.6 x 1.6 cm
Weight
0.43 kg.
ISBN13
9783030746384
Categories

Lebesgue Points and Summability of Higher Dimensional Fourier Series

Ferenc Weisz (Author) · Birkhauser · Paperback

Lebesgue Points and Summability of Higher Dimensional Fourier Series - Weisz, Ferenc

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Synopsis "Lebesgue Points and Summability of Higher Dimensional Fourier Series"

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.

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