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The Convergence And Summability Of Fourier Serico
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Book Synopsis Convergence and Summability of Fourier Transforms and Hardy Spaces by : Ferenc Weisz
Download or read book Convergence and Summability of Fourier Transforms and Hardy Spaces written by Ferenc Weisz and published by Birkhäuser. This book was released on 2017-12-27 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lebesgue Points and Summability of Higher Dimensional Fourier Series by : Ferenc Weisz
Download or read book Lebesgue Points and Summability of Higher Dimensional Fourier Series written by Ferenc Weisz and published by Springer Nature. This book was released on 2021-06-12 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the summability of higher dimensional Fourier series, and generalizes the concept of Lebesgue points. Focusing on Fejér and Cesàro summability, as well as theta-summation, readers will become more familiar with a wide variety of summability methods. Within the theory of higher dimensional summability of Fourier series, the book also provides a much-needed simple proof of Lebesgue’s theorem, filling a gap in the literature. Recent results and real-world applications are highlighted as well, making this a timely resource. The book is structured into four chapters, prioritizing clarity throughout. Chapter One covers basic results from the one-dimensional Fourier series, and offers a clear proof of the Lebesgue theorem. In Chapter Two, convergence and boundedness results for the lq-summability are presented. The restricted and unrestricted rectangular summability are provided in Chapter Three, as well as the sufficient and necessary condition for the norm convergence of the rectangular theta-means. Chapter Four then introduces six types of Lebesgue points for higher dimensional functions. Lebesgue Points and Summability of Higher Dimensional Fourier Series will appeal to researchers working in mathematical analysis, particularly those interested in Fourier and harmonic analysis. Researchers in applied fields will also find this useful.
Book Synopsis Convergence and Summability of Fourier Series by : Pamela Kimm
Download or read book Convergence and Summability of Fourier Series written by Pamela Kimm and published by . This book was released on 1965 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Absolute Summability of Fourier Series and Orthogonal Series by : Y. Okuyama
Download or read book Absolute Summability of Fourier Series and Orthogonal Series written by Y. Okuyama and published by Springer. This book was released on 2006-12-08 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Convergence and Summability of Fourier Serico by : Kenneth L. Cooke
Download or read book The Convergence and Summability of Fourier Serico written by Kenneth L. Cooke and published by . This book was released on 1948 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Sequences, Summability and Fourier Analysis by : S. Nanda
Download or read book Sequences, Summability and Fourier Analysis written by S. Nanda and published by Alpha Science Int'l Ltd.. This book was released on 2005 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sequences, Summability and Fourier Analysis deals with various aspects of summability, a major branch of analysis. The subject grew extensively during the twentieth century through the contribution of eminent analysts, but there are numerous unsolved problems, which still baffle the present-day scholars, as the application side has been poorly attended to. This volume contains original research articles, many valuable survey articles on approximation theory, multivalent functions, almost convergence and absolute almost convergence, Tauberian theorems, Köthe-Toeplitz duals of sequence spaces, random Fourier series, stochastic integrals, interpolative subspaces of Banach space, metric transformations in sequence spaces, absolute summability and Nörlund summability.
Book Synopsis Operators Connected with Convergence and Summability of Fourier Series and Fourier Integrals by : Per Sjölin
Download or read book Operators Connected with Convergence and Summability of Fourier Series and Fourier Integrals written by Per Sjölin and published by . This book was released on 1971 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Classical and Multilinear Harmonic Analysis by : Camil Muscalu
Download or read book Classical and Multilinear Harmonic Analysis written by Camil Muscalu and published by Cambridge University Press. This book was released on 2013-01-31 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.
Book Synopsis Summability Theory and Its Applications by : Robert Ellis Powell
Download or read book Summability Theory and Its Applications written by Robert Ellis Powell and published by . This book was released on 1972 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Operators connected wi9th convergence and summability of Fourier series and Fourier integrals by : Per Sjölin
Download or read book Operators connected wi9th convergence and summability of Fourier series and Fourier integrals written by Per Sjölin and published by . This book was released on 1971 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fourier Analysis by : Elias M. Stein
Download or read book Fourier Analysis written by Elias M. Stein and published by Princeton University Press. This book was released on 2011-02-11 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
Book Synopsis Contributions to Fourier Analysis by : Antoni Zygmund
Download or read book Contributions to Fourier Analysis written by Antoni Zygmund and published by Princeton University Press. This book was released on 1950-08-21 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Contributions to Fourier Analysis. (AM-25), will be forthcoming.
Book Synopsis Trigonometric Fourier Series and Their Conjugates by : L. Zhizhiashvili
Download or read book Trigonometric Fourier Series and Their Conjugates written by L. Zhizhiashvili and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in the theory of trigonometric series has been carried out for over two centuries. The results obtained have greatly influenced various fields of mathematics, mechanics, and physics. Nowadays, the theory of simple trigonometric series has been developed fully enough (we will only mention the monographs by Zygmund [15, 16] and Bari [2]). The achievements in the theory of multiple trigonometric series look rather modest as compared to those in the one-dimensional case though multiple trigonometric series seem to be a natural, interesting and promising object of investigation. We should say, however, that the past few decades have seen a more intensive development of the theory in this field. To form an idea about the theory of multiple trigonometric series, the reader can refer to the surveys by Shapiro [1], Zhizhiashvili [16], [46], Golubov [1], D'yachenko [3]. As to monographs on this topic, only that ofYanushauskas [1] is known to me. This book covers several aspects of the theory of multiple trigonometric Fourier series: the existence and properties of the conjugates and Hilbert transforms of integrable functions; convergence (pointwise and in the LP-norm, p > 0) of Fourier series and their conjugates, as well as their summability by the Cesaro (C,a), a> -1, and Abel-Poisson methods; approximating properties of Cesaro means of Fourier series and their conjugates.
Book Synopsis Theory and Applications of Fourier Analysis by : Charles Sparks Rees
Download or read book Theory and Applications of Fourier Analysis written by Charles Sparks Rees and published by CRC Press. This book was released on 1981-01-01 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Trignometric sums; Integrability of trigonometric sums; Convergence and cesaro summability of fourier series; Convergence and summability of trigonetric series; Multiple fourier series; Fourier transform and applications; Orthogonal systems; Bessel functions.
Book Synopsis Convergence and Summability Problems in the Theory of Fourier Series by : Arlene Marie Jones
Download or read book Convergence and Summability Problems in the Theory of Fourier Series written by Arlene Marie Jones and published by . This book was released on 1979 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Examining the Absolute Rate of Convergence of Summability Assisted Fourier Series by : Brian M. Wright
Download or read book Examining the Absolute Rate of Convergence of Summability Assisted Fourier Series written by Brian M. Wright and published by . This book was released on 2007 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract not available.
Book Synopsis Introduction to Fourier Analysis and Wavelets by : Mark A. Pinsky
Download or read book Introduction to Fourier Analysis and Wavelets written by Mark A. Pinsky and published by American Mathematical Society. This book was released on 2023-12-21 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a concrete introduction to a number of topics in harmonic analysis, accessible at the early graduate level or, in some cases, at an upper undergraduate level. Necessary prerequisites to using the text are rudiments of the Lebesgue measure and integration on the real line. It begins with a thorough treatment of Fourier series on the circle and their applications to approximation theory, probability, and plane geometry (the isoperimetric theorem). Frequently, more than one proof is offered for a given theorem to illustrate the multiplicity of approaches. The second chapter treats the Fourier transform on Euclidean spaces, especially the author's results in the three-dimensional piecewise smooth case, which is distinct from the classical Gibbs–Wilbraham phenomenon of one-dimensional Fourier analysis. The Poisson summation formula treated in Chapter 3 provides an elegant connection between Fourier series on the circle and Fourier transforms on the real line, culminating in Landau's asymptotic formulas for lattice points on a large sphere. Much of modern harmonic analysis is concerned with the behavior of various linear operators on the Lebesgue spaces $L^p(mathbb{R}^n)$. Chapter 4 gives a gentle introduction to these results, using the Riesz–Thorin theorem and the Marcinkiewicz interpolation formula. One of the long-time users of Fourier analysis is probability theory. In Chapter 5 the central limit theorem, iterated log theorem, and Berry–Esseen theorems are developed using the suitable Fourier-analytic tools. The final chapter furnishes a gentle introduction to wavelet theory, depending only on the $L_2$ theory of the Fourier transform (the Plancherel theorem). The basic notions of scale and location parameters demonstrate the flexibility of the wavelet approach to harmonic analysis. The text contains numerous examples and more than 200 exercises, each located in close proximity to the related theoretical material.
