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Pointwise Convergence Of Fourier Series
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Book Synopsis Pointwise Convergence of Fourier Series by : Juan Arias de Reyna
Download or read book Pointwise Convergence of Fourier Series written by Juan Arias de Reyna and published by Springer. This book was released on 2004-10-13 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds. It points out the motivation of every step in the proof. Thus the Carleson-Hunt theorem becomes accessible to any analyst.The book also contains the first detailed exposition of the fine results of Hunt, Sjölin, Soria, etc on the convergence of Fourier Series. Its final chapters present original material. With both Fefferman's proof and the recent one of Lacey and Thiele in print, it becomes more important than ever to understand and compare these two related proofs with that of Carleson and Hunt. These alternative proofs do not yield all the results of the Carleson-Hunt proof. The intention of this monograph is to make Carleson's proof accessible to a wider audience, and to explain its consequences for the pointwise convergence of Fourier series for functions in spaces near $äcal Lü^1$, filling a well-known gap in the literature.
Book Synopsis On the Pointwise Convergence of Fourier Series by : Charles J. Mozzochi
Download or read book On the Pointwise Convergence of Fourier Series written by Charles J. Mozzochi and published by Springer. This book was released on 2006-11-15 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pointwise Convergence of Fourier Series by :
Download or read book Pointwise Convergence of Fourier Series written by and published by . This book was released on 2002 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pointwise Convergence of Fourier Series by : Aongus O. Cairbre
Download or read book Pointwise Convergence of Fourier Series written by Aongus O. Cairbre and published by . This book was released on 1982 with total page 228 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 Pointwise Convergence of Fourier Series on Compact Lie Groups by :
Download or read book Pointwise Convergence of Fourier Series on Compact Lie Groups written by and published by . This book was released on 1990 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pointwise Convergence of Fourier Series on Compact Lie Gropus by : L. Colzani
Download or read book Pointwise Convergence of Fourier Series on Compact Lie Gropus written by L. Colzani and published by . This book was released on 1990 with total page 14 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 An Introduction to Lebesgue Integration and Fourier Series by : Howard J. Wilcox
Download or read book An Introduction to Lebesgue Integration and Fourier Series written by Howard J. Wilcox and published by Courier Corporation. This book was released on 2012-04-30 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects. The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire. Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.
Book Synopsis Pointwise and Uniform Convergence of Fourier Series on SU(2) by : Donald Forrest Myers
Download or read book Pointwise and Uniform Convergence of Fourier Series on SU(2) written by Donald Forrest Myers and published by . This book was released on 2016 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Let f be a Lipschitz function on the special unitary group SU(2). We prove that the Fourier partial sums of f converge to f uniformly on SU(2), thereby extending theorems of Caccioppoli, Mayer, and a special case of Ragozin. Pointwise convergence theorems for the Fourier series of functions on SU(2), due to Liu and Qian, were obtained by Clifford algebra techniques. We obtain similar versions of these theorems using simpler proof techniques: classical harmonic analysis and group theory"--Abstract, page iii.
Book Synopsis An Introduction to Nonharmonic Fourier Series by :
Download or read book An Introduction to Nonharmonic Fourier Series written by and published by Academic Press. This book was released on 1981-01-09 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Nonharmonic Fourier Series
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 Introduction to Fourier Series by : Rupert Lasser
Download or read book Introduction to Fourier Series written by Rupert Lasser and published by CRC Press. This book was released on 1996-02-08 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work addresses all of the major topics in Fourier series, emphasizing the concept of approximate identities and presenting applications, particularly in time series analysis. It stresses throughout the idea of homogenous Banach spaces and provides recent results. Techniques from functional analysis and measure theory are utilized.;College and university bookstores may order five or more copies at a special student price, available on request from Marcel Dekker, Inc.
Book Synopsis Convergence of Fourier Series [and] Uniform Convergence of Fourier Series by : Hubert Evelyn Bray
Download or read book Convergence of Fourier Series [and] Uniform Convergence of Fourier Series written by Hubert Evelyn Bray and published by . This book was released on 1953 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Measure and Integral by : Richard Wheeden
Download or read book Measure and Integral written by Richard Wheeden and published by CRC Press. This book was released on 1977-11-01 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume develops the classical theory of the Lebesgue integral and some of its applications. The integral is initially presented in the context of n-dimensional Euclidean space, following a thorough study of the concepts of outer measure and measure. A more general treatment of the integral, based on an axiomatic approach, is later given.
Book Synopsis Fourier Series, a Modern Introduction by : Robert E. Edwards
Download or read book Fourier Series, a Modern Introduction written by Robert E. Edwards and published by . This book was released on 1979 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Signals and Systems by : Richard Baraniuk
Download or read book Signals and Systems written by Richard Baraniuk and published by Orange Grove Texts Plus. This book was released on 2009-09-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text deals with signals, systems, and transforms, from their theoretical mathematical foundations to practical implementation in circuits and computer algorithms. At its conclusion, learners will have a deep understanding of the mathematics and practical issues of signals in continuous and discrete time, linear time invariant systems, convolution, and Fourier transforms.
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