Summability Calculus - 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 Calculus write by Ibrahim M. Alabdulmohsin. This book was released on 2018-03-07. Summability Calculus available in PDF, EPUB and Kindle. This book develops the foundations of "summability calculus", which is a comprehensive theory of fractional finite sums. It fills an important gap in the literature by unifying and extending disparate historical results. It also presents new material that has not been published before. Importantly, it shows how the study of fractional finite sums benefits from and contributes to many areas of mathematics, such as divergent series, numerical integration, approximation theory, asymptotic methods, special functions, series acceleration, Fourier analysis, the calculus of finite differences, and information theory. As such, it appeals to a wide audience of mathematicians whose interests include the study of special functions, summability theory, analytic number theory, series and sequences, approximation theory, asymptotic expansions, or numerical methods. Richly illustrated, it features chapter summaries, and includes numerous examples and exercises. The content is mostly developed from scratch using only undergraduate mathematics, such as calculus and linear algebra.
Approximation Theory, Sequence Spaces and Applications
Approximation Theory, Sequence Spaces and Applications - 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 Approximation Theory, Sequence Spaces and Applications write by S. A. Mohiuddine. This book was released on 2022-12-07. Approximation Theory, Sequence Spaces and Applications available in PDF, EPUB and Kindle. This book publishes original research chapters on the theory of approximation by positive linear operators as well as theory of sequence spaces and illustrates their applications. Chapters are original and contributed by active researchers in the field of approximation theory and sequence spaces. Each chapter describes the problem of current importance and summarizes ways of their solution and possible applications which improve the current understanding pertaining to sequence spaces and approximation theory. The presentation of the articles is clear and self-contained throughout the book.
Canadian Journal of Mathematics
Canadian Journal of Mathematics - 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 Canadian Journal of Mathematics write by . This book was released on 1969. Canadian Journal of Mathematics available in PDF, EPUB and Kindle.
Convergence and Summability of Fourier Transforms and Hardy Spaces
Convergence and Summability of Fourier Transforms 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 Convergence and Summability of Fourier Transforms and Hardy Spaces write by Ferenc Weisz. This book was released on 2017-12-27. Convergence and Summability of Fourier Transforms and Hardy Spaces available in PDF, EPUB and Kindle. This book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces. To do so, it studies a general summability method known as theta-summation, which encompasses all the well-known summability methods, such as the Fejér, Riesz, Weierstrass, Abel, Picard, Bessel and Rogosinski summations. Following on the classic books by Bary (1964) and Zygmund (1968), this is the first book that considers strong summability introduced by current methodology. A further unique aspect is that the Lebesgue points are also studied in the theory of multi-dimensional summability. In addition to classical results, results from the past 20-30 years – normally only found in scattered research papers – are also gathered and discussed, offering readers a convenient “one-stop” source to support their work. As such, the book will be useful for researchers, graduate and postgraduate students alike.
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].
