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Author: Charles Jean de La Vallée Poussin
Publisher:
ISBN:
Category : Mathematics
Languages : fr
Pages : 644
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Book Description
Author: Charles Jean de La Vallée Poussin
Publisher:
ISBN:
Category : Mathematics
Languages : fr
Pages : 644
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Book Description
Author: P.L. Butzer
Publisher: Birkhäuser
ISBN: 3034874480
Category : Mathematics
Languages : en
Pages : 565
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Book Description
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: Z. Ciesielski
Publisher: Springer Science & Business Media
ISBN: 9789027704832
Category : Mathematics
Languages : en
Pages : 312
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Book Description
Proceedings of the Conference jointly organized by the Mathematical Institute of the Polish Academy of Science and the Institute of Adam Mickiewicz University, held in Poznan, 22-26 August 1972
Author:
Publisher: Academic Press
ISBN: 0080873537
Category : Mathematics
Languages : en
Pages : 573
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Book Description
Fourier Analysis and Approximation
Author: R. S. Varga
Publisher: SIAM
ISBN: 9781611970647
Category : Mathematics
Languages : en
Pages : 81
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Book Description
Surveys the enormous literature on numerical approximation of solutions of elliptic boundary problems by means of variational and finite element methods, requiring almost constant application of results and techniques from functional analysis and approximation theory to the field of numerical analysis.
Author: A. F. Timan
Publisher: Elsevier
ISBN: 1483184811
Category : Mathematics
Languages : en
Pages : 644
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Book Description
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: S.P. Singh
Publisher: Springer Science & Business Media
ISBN: 9401585776
Category : Mathematics
Languages : en
Pages : 580
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Book Description
Approximation Theory, Wavelets and Applications draws together the latest developments in the subject, provides directions for future research, and paves the way for collaborative research. The main topics covered include constructive multivariate approximation, theory of splines, spline wavelets, polynomial and trigonometric wavelets, interpolation theory, polynomial and rational approximation. Among the scientific applications were de-noising using wavelets, including the de-noising of speech and images, and signal and digital image processing. In the area of the approximation of functions the main topics include multivariate interpolation, quasi-interpolation, polynomial approximation with weights, knot removal for scattered data, convergence theorems in Padé theory, Lyapunov theory in approximation, Neville elimination as applied to shape preserving presentation of curves, interpolating positive linear operators, interpolation from a convex subset of Hilbert space, and interpolation on the triangle and simplex. Wavelet theory is growing extremely rapidly and has applications which will interest readers in the physical, medical, engineering and social sciences.
Author: A M Sedletskii
Publisher: CRC Press
ISBN: 9789056992347
Category : Mathematics
Languages : en
Pages : 280
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Book Description
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:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 504
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Book Description
Author: S. Machado
Publisher: Springer
ISBN: 3540385290
Category : Mathematics
Languages : en
Pages : 647
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Book Description
