Ferenc Weisz
Lebesgue Points and Summability of Higher Dimensional Fourier Series
Lebesgue Points and Summability of Higher Dimensional Fourier Series
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- More about Lebesgue Points and Summability of Higher Dimensional Fourier Series
This monograph discusses the summability of higher-dimensional Fourier series and generalizes the concept of Lebesgue points. It focuses on Fejér and Cesàro summability,theta-summation,and provides a simple proof of Lebesgue's theorem. Recent results and real-world applications are highlighted,making it a valuable resource for researchers in mathematical analysis and applied fields.
Format: Hardback
Length: 290 pages
Publication date: 13 June 2021
Publisher: Springer Nature Switzerland AG
This monograph delves into the summability of higher-dimensional Fourier series, expanding the concept of Lebesgue points. By focusing on Fejér and Cesàro summability, as well as theta-summation, readers will gain a comprehensive understanding of various summability methods. Moreover, the book offers a much-needed simple proof of Lebesgue's theorem, filling a gap in the literature. Recent results and real-world applications are highlighted, making this a timely resource.
The book is organized into four chapters, ensuring clarity throughout. Chapter One provides foundational results from one-dimensional Fourier series, presenting a clear proof of Lebesgue's theorem. Chapter Two explores convergence and boundedness results for the lq-summability, while Chapter Three discusses restricted and unrestricted rectangular summability, along with the necessary and sufficient conditions for norm convergence of rectangular theta-means. Chapter Four introduces six types of Lebesgue points for higher-dimensional functions.
Lebesgue Points and Summability of Higher Dimensional Fourier Series is a valuable resource for researchers in mathematical analysis, particularly those interested in Fourier and harmonic analysis. It will also be of interest to researchers in applied fields.
Weight: 623g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030746353
Edition number: 1st ed. 2021
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