Degree of Approximation by Polynomials in the Complex Domain. (AM-9), Volume 9 PDF Download
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Author: Walter Edwin Sewell
Publisher: Princeton University Press
ISBN: 1400882214
Category : Mathematics
Languages : en
Pages : 248
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Book Description
The description for this book, Degree of Approximation by Polynomials in the Complex Domain. (AM-9), Volume 9, will be forthcoming.
Author: Walter Edwin Sewell
Publisher: Princeton University Press
ISBN: 1400882214
Category : Mathematics
Languages : en
Pages : 248
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Book Description
The description for this book, Degree of Approximation by Polynomials in the Complex Domain. (AM-9), Volume 9, will be forthcoming.
Author: Ernest Raymond Johnston
Publisher:
ISBN:
Category : Numerical analysis
Languages : en
Pages : 320
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Author: J. L. Walsh
Publisher: American Mathematical Soc.
ISBN: 0821810200
Category : Mathematics
Languages : en
Pages : 418
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Book Description
The present work is restricted to the representation of functions in the complex domain, particularly analytic functions, by sequences of polynomials or of more general rational functions whose poles are preassigned, the sequences being defined either by interpolation or by extremal properties (i.e. best approximation). Taylor's series plays a central role in this entire study, for it has properties of both interpolation and best approximation, and serves as a guide throughout the whole treatise. Indeed, almost every result given on the representation of functions is concerned with a generalization either of Taylor's series or of some property of Taylor's series--the title ``Generalizations of Taylor's Series'' would be appropriate.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 236
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Author: Joseph Leonard Walsh
Publisher:
ISBN:
Category : Approximate computation
Languages : en
Pages : 104
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Book Description
Author: H N Mhaskar
Publisher: World Scientific
ISBN: 9814518050
Category : Mathematics
Languages : en
Pages : 398
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Book Description
In this book, we have attempted to explain a variety of different techniques and ideas which have contributed to this subject in its course of successive refinements during the last 25 years. There are other books and surveys reviewing the ideas from the perspective of either potential theory or orthogonal polynomials. The main thrust of this book is to introduce the subject from an approximation theory point of view. Thus, the main motivation is to study analogues of results from classical trigonometric approximation theory, introducing other ideas as needed. It is not our objective to survey the most recent results, but merely to introduce to the readers the thought processes and ideas as they are developed.This book is intended to be self-contained, although the reader is expected to be familiar with rudimentary real and complex analysis. It will also help to have studied elementary trigonometric approximation theory, and have some exposure to orthogonal polynomials.
Author: Ralph P.Jr. Boas
Publisher: Springer Science & Business Media
ISBN: 3642878873
Category : Mathematics
Languages : en
Pages : 85
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Book Description
This monograph deals with the expansion properties, in the complex domain, of sets of polynomials which are defined by generating relations. It thus represents a synthesis of two branches of analysis which have been developing almost independently. On the one hand there has grown up a body of results dealing with the more or less formal prop erties of sets of polynomials which possess simple generating relations. Much of this material is summarized in the Bateman compendia (ERDELYI [1J, vol. III, chap. 19) and in TRUESDELL [1J. On the other hand, a problem of fundamental interest in classical analysis is to study the representability of an analytic function j(z) as a series 2::CnPn(z), where {Pn} is a prescribed sequence of functions, and the connections between the function j and the coefficients en. BIEBERBACH'S mono graph Analytisehe Fortsetzung (Ergebnisse der Mathematik, new series, no. 3) can be regarded as a study of this problem for the special choice Pn (z) = zn, and illustrates the depth and detail which such a specializa tion allows. However, the wealth of available information about other sets of polynomials has seldom been put to work in this connection (the application of generating relations to expansion of functions is not even mentioned in the Bateman compendia). At the other extreme, J. M.
Author: Walter Edwin Sewell
Publisher:
ISBN:
Category : Approximation theory
Languages : en
Pages : 236
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Book Description
Author: Ralph P. Boas
Publisher: Springer Science & Business Media
ISBN: 3662251701
Category : Mathematics
Languages : en
Pages : 85
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Book Description
This monograph deals with the expansion properties, in the complex domain, of sets of polynomials which are defined by generating relations. It thus represents a synthesis of two branches of analysis which have been developing almost independently. On the one hand there has grown up a body of results dealing with the more or less formal prop erties of sets of polynomials which possess simple generating relations. Much of this material is summarized in the Bateman compendia (ERDELYI [1], voi. III, chap. 19) and in TRUESDELL [1]. On the other hand, a problem of fundamental interest in classical analysis is to study the representability of an analytic function f(z) as a series ,Lc,. p,. (z), where {p,. } is a prescribed sequence of functions, and the connections between the function f and the coefficients c,. . BIEBERBACH's mono graph Analytische Fortsetzung (Ergebnisse der Mathematik, new series, no. 3) can be regarded as a study of this problem for the special choice p,. (z) =z", and illustrates the depth and detail which such a specializa tion allows. However, the wealth of available information about other sets of polynomials has seldom been put to work in this connection (the application of generating relations to expansion of functions is not even mentioned in the Bateman compendia). At the other extreme, J. M.
Author: Joseph Leonard Walsh (Mathematiker)
Publisher:
ISBN:
Category :
Languages : fr
Pages : 72
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Book Description
