Martingale Hardy Spaces and Summability of One-Dimensional Vilenkin-Fourier Series - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Martingale Hardy Spaces and Summability of One-Dimensional Vilenkin-Fourier Series write by Lars-Erik Persson. This book was released on 2022-11-22. Martingale Hardy Spaces and Summability of One-Dimensional Vilenkin-Fourier Series available in PDF, EPUB and Kindle. 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.
Martingale Hardy Spaces and their Applications in Fourier Analysis
Martingale Hardy Spaces and their Applications in Fourier Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Martingale Hardy Spaces and their Applications in Fourier Analysis write by Ferenc Weisz. This book was released on 2006-11-15. Martingale Hardy Spaces and their Applications in Fourier Analysis available in PDF, EPUB and Kindle. This book deals with the theory of one- and two-parameter martingale Hardy spaces and their use in Fourier analysis, and gives a summary of the latest results in this field. A method that can be applied for both one- and two-parameter cases, the so-called atomic decomposition method, is improved and provides a new and common construction of the theory of one- and two-parameter martingale Hardy spaces. A new proof of Carleson's convergence result using martingale methods for Fourier series is given with martingale methods. The book is accessible to readers familiar with the fundamentals of probability theory and analysis. It is intended for researchers and graduate students interested in martingale theory, Fourier analysis and in the relation between them.
Summability of Multi-Dimensional Fourier Series and Hardy Spaces
Summability of Multi-Dimensional Fourier Series and Hardy Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Summability of Multi-Dimensional Fourier Series and Hardy Spaces write by Ferenc Weisz. This book was released on 2013-06-29. Summability of Multi-Dimensional Fourier Series and Hardy Spaces available in PDF, EPUB and Kindle. The history of martingale theory goes back to the early fifties when Doob [57] pointed out the connection between martingales and analytic functions. On the basis of Burkholder's scientific achievements the mar tingale theory can perfectly well be applied in complex analysis and in the theory of classical Hardy spaces. This connection is the main point of Durrett's book [60]. The martingale theory can also be well applied in stochastics and mathematical finance. The theories of the one-parameter martingale and the classical Hardy spaces are discussed exhaustively in the literature (see Garsia [83], Neveu [138], Dellacherie and Meyer [54, 55], Long [124], Weisz [216] and Duren [59], Stein [193, 194], Stein and Weiss [192], Lu [125], Uchiyama [205]). The theory of more-parameter martingales and martingale Hardy spaces is investigated in Imkeller [107] and Weisz [216]. This is the first mono graph which considers the theory of more-parameter classical Hardy spaces. The methods of proofs for one and several parameters are en tirely different; in most cases the theorems stated for several parameters are much more difficult to verify. The so-called atomic decomposition method that can be applied both in the one-and more-parameter cases, was considered for martingales by the author in [216].
Tbilisi Analysis and PDE Seminar
Tbilisi Analysis and PDE Seminar - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Tbilisi Analysis and PDE Seminar write by Roland Duduchava. This book was released on . Tbilisi Analysis and PDE Seminar available in PDF, EPUB and Kindle.
Extended Abstracts 2021/2022
Extended Abstracts 2021/2022 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Extended Abstracts 2021/2022 write by Duván Cardona. This book was released on . Extended Abstracts 2021/2022 available in PDF, EPUB and Kindle.
