Lebesgue points and summability of higher dimensional Fourier series

書誌事項

Lebesgue points and summability of higher dimensional Fourier series

Ferenc Weisz

Birkhäuser, c2021

  • : pbk

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注記

Includes bibliographical references (p. 271-284) and index

内容説明・目次

内容説明

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.

目次

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

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詳細情報

  • NII書誌ID(NCID)
    BC18940445
  • ISBN
    • 9783030746384
  • 出版国コード
    sz
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    [Cham]
  • ページ数/冊数
    xiii, 290 p.
  • 大きさ
    24 cm
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