Martingale Hardy Spaces and Summability of One-Dimensional Vilenkin-Fourier Series

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Lars-Erik Persson George Tephnadze

Martingale Hardy Spaces and Summability of One-Dimensional Vilenkin-Fourier Series

Lars-Erik Persson, George Tephnadze, Ferenc Weisz

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English

Birkhauser Verlag AG
23 November 2023

Calculus & mathematical analysis; Complex analysis, complex variables; Functional analysis & transforms

This book discusses, develops and applies the theory of Vilenkin-Fourier series connected to modern harmonic analysis.

The classical theory of Fourier series deals with decomposition of a function into sinusoidal waves. Unlike these continuous waves the Vilenkin (Walsh) functions are rectangular waves. Such waves have already been used frequently in the theory of signal transmission, multiplexing, filtering, image enhancement, code theory, digital signal processing and pattern recognition. The development of the theory of Vilenkin-Fourier series has been strongly influenced by the classical theory of trigonometric series. Because of this it is inevitable to compare results of Vilenkin-Fourier series to those on trigonometric series. There are many similarities between these theories, but there exist differences also. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group. The first part of the book can be used as an introduction to the subject, and the following chapters summarize the most recent research in this fascinating area and can be read independently. Each chapter concludes with historical remarks and open questions. The book will appeal to researchers working in Fourier and more broad harmonic analysis and will inspire them for their own and their students' research. Moreover, researchers in applied fields will appreciate it as a sourcebook far beyond the traditional mathematical domains.

By: Lars-Erik Persson, George Tephnadze, Ferenc Weisz
Imprint: Birkhauser Verlag AG
Country of Publication: Switzerland
Edition: 2022 ed.
Dimensions: Height: 235mm, Width: 155mm,
Weight: 973g
ISBN: 9783031144615
ISBN 10: 3031144619
Pages: 626
Publication Date: 23 November 2023
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Reviews for Martingale Hardy Spaces and Summability of One-Dimensional Vilenkin-Fourier Series

“The book offers a wonderful overview, very well structured and complete, on the theory of harmonic analysis developed in the context of the Vilenkin-Fourier series. … each chapter begins with a broad introduction rich in bibliographical citations that allow the reader to locate himself in the historical context of the topics to be addressed … the authors include an important and interesting list of open problems proposed with a view to being resolved in future research.” (Iris Athamaica López Palacios, zbMATH 1512.42042, 2023)