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ISBN: 3031144597 3031144589 Year: 2022 Publisher: Cham, Switzerland : Birkhäuser,
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Fourier series. --- Hardy spaces. --- Martingales (Mathematics) --- Sèries de Fourier --- Espais de Hardy --- Martingales (Matemàtica) --- Stochastic processes --- Spaces, Hardy --- Functional analysis --- Functions of complex variables --- Fourier integrals --- Series, Fourier --- Series, Trigonometric --- Trigonometric series --- Calculus --- Fourier analysis --- Harmonic analysis --- Harmonic functions --- Processos estocàstics --- Hardy, Espacios de --- Anàlisi funcional --- Integrals de Fourier --- Sèries trigonomètriques --- Anàlisi de Fourier --- Càlcul --- Integrals de Dirichlet
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ISBN: 9783031144592 9783031144585 9783031144608 9783031144615 Year: 2022 Publisher: Cham Springer International Publishing :Imprint: Birkhäuser
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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.
Harmonic analysis. Fourier analysis --- Mathematical analysis --- Mathematics --- Fourieranalyse --- analyse (wiskunde) --- reeksen (wiskunde) --- Fourierreeksen --- mathematische modellen --- wiskunde
Book
ISBN: 9783031628948 Year: 2024 Publisher: Cham Springer Nature Switzerland :Imprint: Birkhäuser
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The aim of this volume is to present some new developments and ideas in partial differential equations and mathematical analysis, including spectral analysis and boundary value problems for PDE, harmonic analysis, inequalities, integral equations, and applications. This book is a collection of short summaries of reports from lectures delivered at Tbilisi Analysis & PDE seminars and workshops. In particular, it contains some applications and several open questions aimed at inspiring further research. The volume contains 21 research articles.
Mathematical analysis. --- Differential equations. --- Integral equations. --- Analysis. --- Differential Equations. --- Integral Equations.
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