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Lebesgue Points and Summability of Higher Dimensional Fourier Series

Authors: Weisz, Ferenc

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  • Presents the summability of higher dimensional Fourier series, and generalizes the concept of Lebesgue points
  • Introduces readers to multiple methods of summability, focusing particularly on Fejér and Cesàro summability, as well as theta-summation
  • Includes multiple real-world applications, recent results, and a presentation that prioritizes clarity throughout
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eBook $109.00
price for USA in USD
  • ISBN 978-3-030-74636-0
  • Digitally watermarked, DRM-free
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  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-3-030-74635-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
About this book

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.

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $109.00
price for USA in USD
  • ISBN 978-3-030-74636-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-3-030-74635-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Lebesgue Points and Summability of Higher Dimensional Fourier Series
Authors
Copyright
2021
Publisher
Birkhäuser Basel
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-74636-0
DOI
10.1007/978-3-030-74636-0
Hardcover ISBN
978-3-030-74635-3
Edition Number
1
Number of Pages
XIII, 290
Number of Illustrations
23 b/w illustrations, 1 illustrations in colour
Topics