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Author : F. Turner
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (643 download)
Download or read book Some Aspects of Fourier Series and Trigonometric Interpolation written by F. Turner and published by . This book was released on 1974 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Antoni Zygmund
Publisher : Cambridge University Press
ISBN 13 : 9780521890533
Total Pages : 784 pages
Book Rating : 4.8/5 (95 download)
Download or read book Trigonometric Series written by Antoni Zygmund and published by Cambridge University Press. This book was released on 2002 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: Both volumes of classic text on trigonometric series, with a foreword by Robert Fefferman.
Author : Antoni Zygmund
Publisher :
ISBN 13 :
Total Pages : 208 pages
Book Rating : 4.F/5 ( download)
Download or read book Trigonometric Interpolation ... written by Antoni Zygmund and published by . This book was released on 1950 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Wen L. Li
Publisher : CRC Press
ISBN 13 : 1000781097
Total Pages : 368 pages
Book Rating : 4.0/5 (7 download)
Download or read book Fourier Methods in Science and Engineering written by Wen L. Li and published by CRC Press. This book was released on 2022-11-21 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This innovative book discusses and applies the generalized Fourier Series to a variety of problems commonly encountered within science and engineering, equipping the readers with a clear pathway through which to use the Fourier methods as a solution technique for a wide range of differential equations and boundary value problems. Beginning with an overview of the conventional Fourier series theory, this book introduces the generalized Fourier series (GFS), emphasizing its notable rate of convergence when compared to the conventional Fourier series expansions. After systematically presenting the GFS as a powerful and unified solution method for ordinary differential equations and partial differential equations, this book expands on some representative boundary value problems, diving into their multiscale characteristics. This book will provide readers with the comprehensive foundation necessary for solving a wide spectrum of mathematical problems key to practical applications. It will also be of interest to researchers, engineers, and college students in various science, engineering, and mathematics fields.
Author : L. Zhizhiashvili
Publisher : Springer Science & Business Media
ISBN 13 : 9400902832
Total Pages : 314 pages
Book Rating : 4.4/5 (9 download)
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.
Author : Cornelius Lanczos
Publisher : SIAM
ISBN 13 : 1611974526
Total Pages : 272 pages
Book Rating : 4.6/5 (119 download)
Download or read book Discourse on Fourier Series written by Cornelius Lanczos and published by SIAM. This book was released on 2016-09-09 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1966, this well-written and still-cited text covers Fourier analysis, a foundation of science and engineering. Many modern textbooks are filled with specialized terms and equations that may be confusing, but this book uses a friendly, conversational tone to clarify the material and engage the reader. The author meticulously develops the topic and uses 161 problems integrated into the text to walk the student down the simplest path to a solution. Intended for students of engineering, physics, and mathematics at both advanced undergraduate and graduate levels.
Author : Sergei Suslov
Publisher : Springer Science & Business Media
ISBN 13 : 1475737319
Total Pages : 379 pages
Book Rating : 4.4/5 (757 download)
Download or read book An Introduction to Basic Fourier Series written by Sergei Suslov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: It was with the publication of Norbert Wiener's book ''The Fourier In tegral and Certain of Its Applications" [165] in 1933 by Cambridge Univer sity Press that the mathematical community came to realize that there is an alternative approach to the study of c1assical Fourier Analysis, namely, through the theory of c1assical orthogonal polynomials. Little would he know at that time that this little idea of his would help usher in a new and exiting branch of c1assical analysis called q-Fourier Analysis. Attempts at finding q-analogs of Fourier and other related transforms were made by other authors, but it took the mathematical insight and instincts of none other then Richard Askey, the grand master of Special Functions and Orthogonal Polynomials, to see the natural connection between orthogonal polynomials and a systematic theory of q-Fourier Analysis. The paper that he wrote in 1993 with N. M. Atakishiyev and S. K Suslov, entitled "An Analog of the Fourier Transform for a q-Harmonic Oscillator" [13], was probably the first significant publication in this area. The Poisson k~rnel for the contin uous q-Hermite polynomials plays a role of the q-exponential function for the analog of the Fourier integral under considerationj see also [14] for an extension of the q-Fourier transform to the general case of Askey-Wilson polynomials. (Another important ingredient of the q-Fourier Analysis, that deserves thorough investigation, is the theory of q-Fourier series.
Author : William O. Bray
Publisher : CRC Press
ISBN 13 : 1000153681
Total Pages : 468 pages
Book Rating : 4.0/5 (1 download)
Download or read book Fourier Analysis written by William O. Bray and published by CRC Press. This book was released on 2020-12-17 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing complete expository and research papers on the geometric and analytic aspects of Fourier analysis, this work discusses new approaches to classical problems in the theory of trigonometric series, singular integrals/pseudo-differential operators, Fourier analysis on various groups, numerical aspects of Fourier analysis and their applications, wavelets and more.
Author : Brad G. Osgood
Publisher : American Mathematical Soc.
ISBN 13 : 1470441918
Total Pages : 689 pages
Book Rating : 4.4/5 (74 download)
Download or read book Lectures on the Fourier Transform and Its Applications written by Brad G. Osgood and published by American Mathematical Soc.. This book was released on 2019-01-18 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is derived from lecture notes for a course on Fourier analysis for engineering and science students at the advanced undergraduate or beginning graduate level. Beyond teaching specific topics and techniques—all of which are important in many areas of engineering and science—the author's goal is to help engineering and science students cultivate more advanced mathematical know-how and increase confidence in learning and using mathematics, as well as appreciate the coherence of the subject. He promises the readers a little magic on every page. The section headings are all recognizable to mathematicians, but the arrangement and emphasis are directed toward students from other disciplines. The material also serves as a foundation for advanced courses in signal processing and imaging. There are over 200 problems, many of which are oriented to applications, and a number use standard software. An unusual feature for courses meant for engineers is a more detailed and accessible treatment of distributions and the generalized Fourier transform. There is also more coverage of higher-dimensional phenomena than is found in most books at this level.
Author : Mark A. Pinsky
Publisher : American Mathematical Society
ISBN 13 : 1470475677
Total Pages : 398 pages
Book Rating : 4.4/5 (74 download)
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.
Author : N. W. Gowar
Publisher :
ISBN 13 :
Total Pages : 158 pages
Book Rating : 4.:/5 (318 download)
Download or read book Fourier Series written by N. W. Gowar and published by . This book was released on 1974 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Canadian Mathematical Bulletin written by and published by . This book was released on 1960 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Raymond Edward Alan Christopher Paley
Publisher : American Mathematical Soc.
ISBN 13 : 0821810197
Total Pages : 196 pages
Book Rating : 4.8/5 (218 download)
Download or read book Fourier Transforms in the Complex Domain written by Raymond Edward Alan Christopher Paley and published by American Mathematical Soc.. This book was released on 1934-12-31 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the aid of Fourier-Mellin transforms as a tool in analysis, the authors were able to attack such diverse analytic questions as those of quasi-analytic functions, Mercer's theorem on summability, Milne's integral equation of radiative equilibrium, the theorems of Munz and Szasz concerning the closure of sets of powers of an argument, Titchmarsh's theory of entire functions of semi-exponential type with real negative zeros, trigonometric interpolation and developments in polynomials of the form $\sum^N_1A_ne^{i\lambda_nx}$, lacunary series, generalized harmonic analysis in the complex domain, the zeros of random functions, and many others.
Author : P.L. Butzer
Publisher : Birkhäuser
ISBN 13 : 3034874480
Total Pages : 565 pages
Book Rating : 4.0/5 (348 download)
Download or read book Fourier Analysis and Approximation written by P.L. Butzer and published by Birkhäuser. This book was released on 2012-12-06 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the international conference on 'Harmonic Analysis and Integral Transforms', conducted by one of the authors at the Mathematical Research Institute in Oberwolfach (Black Forest) in August 1965, it was felt that there was a real need for a book on Fourier analysis stressing (i) parallel treatment of Fourier series and Fourier trans forms from a transform point of view, (ii) treatment of Fourier transforms in LP(lRn)_ space not only for p = 1 and p = 2, (iii) classical solution of partial differential equations with completely rigorous proofs, (iv) theory of singular integrals of convolu tion type, (v) applications to approximation theory including saturation theory, (vi) multiplier theory, (vii) Hilbert transforms, Riesz fractional integrals, Bessel potentials, (viii) Fourier transform methods on locally compact groups. This study aims to consider these aspects, presenting a systematic treatment of Fourier analysis on the circle as well as on the infinite line, and of those areas of approximation theory which are in some way or other related thereto. A second volume is in preparation which goes beyond the one-dimensional theory presented here to cover the subject for functions of several variables. Approximately a half of this first volume deals with the theories of Fourier series and of Fourier integrals from a transform point of view.
Author : James S. Walker
Publisher : CRC Press
ISBN 13 : 1351448889
Total Pages : 464 pages
Book Rating : 4.3/5 (514 download)
Download or read book Fast Fourier Transforms written by James S. Walker and published by CRC Press. This book was released on 2017-11-22 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of an indispensable text provides a clear treatment of Fourier Series, Fourier Transforms, and FFTs. The unique software, included with the book and newly updated for this edition, allows the reader to generate, firsthand, images of all aspects of Fourier analysis described in the text. Topics covered include :
Author : Ronald Newbold Bracewell
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (22 download)
Download or read book The Fourier Transform and Its Applications written by Ronald Newbold Bracewell and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : James S. Walker
Publisher : CRC Press
ISBN 13 : 9780849371639
Total Pages : 468 pages
Book Rating : 4.3/5 (716 download)
Download or read book Fast Fourier Transforms, Second Edition written by James S. Walker and published by CRC Press. This book was released on 1996-08-22 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of an indispensable text provides a clear treatment of Fourier Series, Fourier Transforms, and FFTs. The unique software, included with the book and newly updated for this edition, allows the reader to generate, firsthand, images of all aspects of Fourier analysis described in the text. Topics covered include :
