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＜電子ブック＞
Lebesgue Points and Summability of Higher Dimensional Fourier Series / by Ferenc Weisz

版	1st ed. 2021.
出版者	(Cham : Springer International Publishing : Imprint: Birkhäuser)
出版年	2021
大きさ	XIII, 290 p. 24 illus., 1 illus. in color : online resource
著者標目	*Weisz, Ferenc author SpringerLink (Online service)
件　名	LCSH:Fourier analysis LCSH:Sequences (Mathematics) LCSH:Measure theory FREE:Fourier Analysis FREE:Sequences, Series, Summability FREE:Measure and Integration
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-030-74636-0

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