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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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Martingale Hardy Spaces and Summability of One-Dimensional Vilenkin-Fourier Series (Hardcover, 1st ed. 2022)
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Martingale Hardy Spaces and Summability of One-Dimensional Vilenkin-Fourier Series (Hardcover, 1st ed. 2022)
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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.
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