Fourier Analysis And Approximation Of Functions

Author : Roald M. Trigub,Eduard S. Belinsky
Publisher : Springer Science & Business Media
Page : 595 pages
File Size : 48,5 Mb
Release : 2012-11-07
Category : Mathematics
ISBN : 9781402028762

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Fourier Analysis and Approximation of Functions by Roald M. Trigub,Eduard S. Belinsky Pdf

In Fourier Analysis and Approximation of Functions basics of classical Fourier Analysis are given as well as those of approximation by polynomials, splines and entire functions of exponential type. In Chapter 1 which has an introductory nature, theorems on convergence, in that or another sense, of integral operators are given. In Chapter 2 basic properties of simple and multiple Fourier series are discussed, while in Chapter 3 those of Fourier integrals are studied. The first three chapters as well as partially Chapter 4 and classical Wiener, Bochner, Bernstein, Khintchin, and Beurling theorems in Chapter 6 might be interesting and available to all familiar with fundamentals of integration theory and elements of Complex Analysis and Operator Theory. Applied mathematicians interested in harmonic analysis and/or numerical methods based on ideas of Approximation Theory are among them. In Chapters 6-11 very recent results are sometimes given in certain directions. Many of these results have never appeared as a book or certain consistent part of a book and can be found only in periodics; looking for them in numerous journals might be quite onerous, thus this book may work as a reference source. The methods used in the book are those of classical analysis, Fourier Analysis in finite-dimensional Euclidean space Diophantine Analysis, and random choice.

Author : P.L. Butzer,Nessel,Trebels
Publisher : Birkhäuser
Page : 565 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034874489

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Fourier Analysis and Approximation by P.L. Butzer,Nessel,Trebels Pdf

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 : Michael Ruzhansky,Sergey Tikhonov
Publisher : Birkhäuser
Page : 258 pages
File Size : 53,7 Mb
Release : 2016-03-11
Category : Mathematics
ISBN : 9783319274669

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Methods of Fourier Analysis and Approximation Theory by Michael Ruzhansky,Sergey Tikhonov Pdf

Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.

Author : Anonim
Publisher : Academic Press
Page : 554 pages
File Size : 46,7 Mb
Release : 2011-09-21
Category : Mathematics
ISBN : 0080873537

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Fourier Analysis and Approximation by Anonim Pdf

Fourier Analysis and Approximation

Author : György Alexits,Paul Turán
Publisher : North-Holland
Page : 468 pages
File Size : 51,9 Mb
Release : 1978
Category : Mathematics
ISBN : UOM:39015028049982

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Fourier Analysis and Approximation Theory by György Alexits,Paul Turán Pdf

Author : Paul Leo Butzer,Rolf Joachim Nessel
Publisher : Unknown
Page : 553 pages
File Size : 53,7 Mb
Release : 1971
Category : Mathematics
ISBN : 0121485013

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Fourier Analysis and Approximation by Paul Leo Butzer,Rolf Joachim Nessel Pdf

Author : György Alexits,Paul Turán
Publisher : Unknown
Page : 476 pages
File Size : 46,8 Mb
Release : 1978
Category : Approximation theory
ISBN : UOM:39015037744045

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Fourier Analysis and Approximation Theory by György Alexits,Paul Turán Pdf

Author : Volker Michel
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 47,5 Mb
Release : 2012-12-12
Category : Mathematics
ISBN : 9780817684037

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Lectures on Constructive Approximation by Volker Michel Pdf

Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author’s lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets. Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth’s or the brain’s interior. Specific topics covered include: * the advantages and disadvantages of Fourier, spline, and wavelet methods * theory and numerics of orthogonal polynomials on intervals, spheres, and balls * cubic splines and splines based on reproducing kernels * multiresolution analysis using wavelets and scaling functions This textbook is written for students in mathematics, physics, engineering, and the geosciences who have a basic background in analysis and linear algebra. The work may also be suitable as a self-study resource for researchers in the above-mentioned fields.

Author : David W. Kammler
Publisher : Cambridge University Press
Page : 39 pages
File Size : 53,8 Mb
Release : 2008-01-17
Category : Mathematics
ISBN : 9781139469036

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A First Course in Fourier Analysis by David W. Kammler Pdf

This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.

Author : Sergei Suslov
Publisher : Springer Science & Business Media
Page : 379 pages
File Size : 46,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475737318

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An Introduction to Basic Fourier Series by Sergei Suslov Pdf

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 : Paul Leo Butzer,Rolf J. Nessel
Publisher : Unknown
Page : 553 pages
File Size : 52,6 Mb
Release : 1971
Category : Electronic
ISBN : OCLC:1014535996

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Fourier Analysis and Approximation. Vol. 1 by Paul Leo Butzer,Rolf J. Nessel Pdf

Author : R. Vichnevetsky,J. B. Bowles
Publisher : SIAM
Page : 146 pages
File Size : 48,5 Mb
Release : 1982-01-01
Category : Technology & Engineering
ISBN : 9780898713923

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Fourier Analysis of Numerical Approximations of Hyperbolic Equations by R. Vichnevetsky,J. B. Bowles Pdf

This book provides useful reference material for those concerned with the use of Fourier analysis and computational fluid dynamics.

Author : A.J. Jerri
Publisher : Springer Science & Business Media
Page : 357 pages
File Size : 55,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475728477

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The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations by A.J. Jerri Pdf

This book represents the first attempt at a unified picture for the pres ence of the Gibbs (or Gibbs-Wilbraham) phenomenon in applications, its analysis and the different methods of filtering it out. The analysis and filtering cover the familiar Gibbs phenomenon in Fourier series and integral representations of functions with jump discontinuities. In ad dition it will include other representations, such as general orthogonal series expansions, general integral transforms, splines approximation, and continuous as well as discrete wavelet approximations. The mate rial in this book is presented in a manner accessible to upperclassmen and graduate students in science and engineering, as well as researchers who may face the Gibbs phenomenon in the varied applications that in volve the Fourier and the other approximations of functions with jump discontinuities. Those with more advanced backgrounds in analysis will find basic material, results, and motivations from which they can begin to develop deeper and more general results. We must emphasize that the aim of this book (the first on the sUbject): to satisfy such a diverse audience, is quite difficult. In particular, our detailed derivations and their illustrations for an introductory book may very well sound repeti tive to the experts in the field who are expecting a research monograph. To answer the concern of the researchers, we can only hope that this book will prove helpful as a basic reference for their research papers.

Author : A M Sedletskii
Publisher : CRC Press
Page : 280 pages
File Size : 52,7 Mb
Release : 2000-09-20
Category : Mathematics
ISBN : 9056992341

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Fourier Transforms and Approximations by A M Sedletskii Pdf

Three classes of Fourier transforms are presented: Fourier (Laplace) transforms on the halfline, Fourier transforms of measures with compact support and Fourier transforms of rapidly decreasing functions (on whole line). The focus is on the behaviour of Fourier transforms in the region of analyticity and the distribution of their zeros. Applications of results are presented: approximation by exponentials on the finite interval; behavior of the nonharmonic Fourier series; Müntz-Szasz's problem of approximation by powers on unit interval; approximation by weighted exponentials on whole line.

Author : Sir M. J. Lighthill
Publisher : Cambridge University Press
Page : 112 pages
File Size : 44,6 Mb
Release : 1958
Category : Mathematics
ISBN : 0521091284

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An Introduction to Fourier Analysis and Generalised Functions by Sir M. J. Lighthill Pdf

"Clearly and attractively written, but without any deviation from rigorous standards of mathematical proof...." Science Progress