Lebesgue Points and Summability of Higher Dimensional Fourier Series - Couverture rigide

Weisz, Ferenc

Couverture rigide

ISBN 10 : 3030746356 ISBN 13 : 9783030746353

Editeur : Springer Nature Switzerland AG, 2021

Synopsis

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 l_q-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.

Détails de l'édition

• Éditeur: Springer Nature Switzerland AG
• Date d'édition: 2021
• Langue: anglais
• ISBN 10: 3030746356
• ISBN 13: 9783030746353
• Reliure: Relié
• Nombre de pages: 303
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne