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Author : Charles Jean de La Vallée Poussin
Publisher : Unknown
Page : 644 pages
File Size : 55,7 Mb
Release : 2004
Category : Mathematics
ISBN : UOM:39015059578586
Author : Michael Ruzhansky,Sergey Tikhonov
Publisher : Birkhäuser
Page : 258 pages
File Size : 46,8 Mb
Release : 2016-03-11
Category : Mathematics
ISBN : 9783319274669
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 : Roald M. Trigub,Eduard S. Belinsky
Publisher : Springer Science & Business Media
Page : 595 pages
File Size : 48,6 Mb
Release : 2012-11-07
Category : Mathematics
ISBN : 9781402028762
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 : György Alexits,Paul Turán
Publisher : North-Holland
Page : 468 pages
File Size : 44,6 Mb
Release : 1978
Category : Mathematics
ISBN : UOM:39015028049982
Author : A. F. Timan
Publisher : Elsevier
Page : 644 pages
File Size : 53,6 Mb
Release : 2014-07-22
Category : Mathematics
ISBN : 9781483184814
Theory of Approximation of Functions of a Real Variable discusses a number of fundamental parts of the modern theory of approximation of functions of a real variable. The material is grouped around the problem of the connection between the best approximation of functions to their structural properties. This text is composed of eight chapters that highlight the relationship between the various structural properties of real functions and the character of possible approximations to them by polynomials and other functions of simple construction. Each chapter concludes with a section containing various problems and theorems, which supplement the main text. The first chapters tackle the Weierstrass's theorem, the best approximation by polynomials on a finite segment, and some compact classes of functions and their structural properties. The subsequent chapters describe some properties of algebraic polynomials and transcendental integral functions of exponential type, as well as the direct theorems of the constructive theory of functions. These topics are followed by discussions of differential and constructive characteristics of converse theorems. The final chapters explore other theorems connecting the best approximations functions with their structural properties. These chapters also deal with the linear processes of approximation of functions by polynomials. The book is intended for post-graduate students and for mathematical students taking advanced courses, as well as to workers in the field of the theory of functions.
Author : Anonim
Publisher : Academic Press
Page : 554 pages
File Size : 55,8 Mb
Release : 2011-09-21
Category : Mathematics
ISBN : 0080873537
Fourier Analysis and Approximation
Author : Raymond Edward Alan Christopher Paley,Norbert Wiener
Publisher : American Mathematical Soc.
Page : 196 pages
File Size : 47,9 Mb
Release : 1934-12-31
Category : Mathematics
ISBN : 9780821810194
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 : T. W. Körner
Publisher : Cambridge University Press
Page : 400 pages
File Size : 55,8 Mb
Release : 1993-08-19
Category : Mathematics
ISBN : 0521438497
For physicists, engineers and mathematicians, Fourier analysis constitutes a tool of great usefulness. A wide variety of the techniques and applications of the subject were discussed in Dr Körner's highly popular book, Fourier Analysis. Now Dr Körner has compiled a collection of exercises on Fourier analysis that will thoroughly test the understanding of the reader. They are arranged chapter by chapter to correspond with Fourier Analysis, and for all who enjoyed that book, this companion volume will be an essential purchase.
Author : Paul Butzer,Nessel,Trebels
Publisher : Birkhäuser
Page : 554 pages
File Size : 42,7 Mb
Release : 1971-01-01
Category : Mathematics
ISBN : 3764305207
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 : Jayakumar Ramanathan
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461217565
Author : György Alexits,Paul Turán
Publisher : Unknown
Page : 476 pages
File Size : 46,8 Mb
Release : 1978
Category : Approximation theory
ISBN : UOM:39015037744045
Author : V. G. Mazʹi︠a︡,Gunther Schmidt
Publisher : American Mathematical Soc.
Page : 368 pages
File Size : 53,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821842034
In this book, a new approach to approximation procedures is developed. This new approach is characterized by the common feature that the procedures are accurate without being convergent as the mesh size tends to zero. This lack of convergence is compensated for by the flexibility in the choice of approximating functions, the simplicity of multi-dimensional generalizations, and the possibility of obtaining explicit formulas for the values of various integral and pseudodifferential operators applied to approximating functions. The developed techniques allow the authors to design new classes of high-order quadrature formulas for integral and pseudodifferential operators, to introduce the concept of approximate wavelets, and to develop new efficient numerical and semi-numerical methods for solving boundary value problems of mathematical physics. The book is intended for researchers interested in approximation theory and numerical methods for partial differential and integral equations.
Author : P.L. Butzer,Nessel,Trebels
Publisher : Birkhäuser
Page : 565 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034874489
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 : Elliott Ward Cheney,C. K. Chui,Larry L. Schumaker
Publisher : Unknown
Page : 280 pages
File Size : 46,5 Mb
Release : 1993
Category : Mathematics
ISBN : UOM:39015020856848
Author : Paul Leo Butzer,Rolf Joachim Nessel
Publisher : Unknown
Page : 553 pages
File Size : 48,9 Mb
Release : 1971
Category : Mathematics
ISBN : 0121485013