A Generalization of Faber's Polynomials PDF Download
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Author: Joseph Leonard Walsh
Publisher:
ISBN:
Category : Polynomials
Languages : en
Pages : 44
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Book Description
Author: Joseph Leonard Walsh
Publisher:
ISBN:
Category : Polynomials
Languages : en
Pages : 44
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Book Description
Author: P.K. Suetin
Publisher: CRC Press
ISBN: 9789056990589
Category : Mathematics
Languages : en
Pages : 272
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Book Description
Presents some important classical and modern results of the series of Faber polynomials and their applications. Interest in this subject has increased rapidly over the last decade, although the presentation of research has, until now, been confined mainly to journal articles. Applications include theory of functions of complex variables, theory of analytic function approximation, and some aspects of numerical analysis.
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: Pavel Kondratʹevich Suetin
Publisher: American Mathematical Soc.
ISBN: 9780821830000
Category : Mathematics
Languages : en
Pages : 100
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Book Description
Discusses orthogonal polynomials.
Author: Amnon Jakimovski
Publisher: Springer Science & Business Media
ISBN: 1402041756
Category : Mathematics
Languages : en
Pages : 303
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Book Description
This book is a collection of the various old and new results, centered around the following simple and beautiful observation of J.L. Walsh - If a function is analytic in a finite disc, and not in a larger disc, then the difference between the Lagrange interpolant of the function, at the roots of unity, and the partial sums of the Taylor series, about the origin, tends to zero in a larger disc than the radius of convergence of the Taylor series, while each of these operators converges only in the original disc. This book will be particularly useful for researchers in approximation and interpolation theory.
Author: Michiel Hazewinkel
Publisher: Springer
ISBN: 9400959834
Category : Mathematics
Languages : en
Pages : 732
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Book Description
Author: Magnus Rudolph Hestenes
Publisher:
ISBN:
Category : Numerical analysis
Languages : en
Pages : 208
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Book Description
Author: Yu.I. Lyubich
Publisher: Springer Science & Business Media
ISBN: 3662028492
Category : Mathematics
Languages : en
Pages : 290
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Book Description
The twentieth-century view of the analysis of functions is dominated by the study of classes of functions. This volume of the Encyclopaedia covers the origins, development and applications of linear functional analysis, explaining along the way how one is led naturally to the modern approach.
Author: Tobin A. Driscoll
Publisher: Cambridge University Press
ISBN: 9781139433921
Category : Mathematics
Languages : en
Pages : 154
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Book Description
This book provides a comprehensive look at the Schwarz-Christoffel transformation, including its history and foundations, practical computation, common and less common variations, and many applications in fields such as electromagnetism, fluid flow, design and inverse problems, and the solution of linear systems of equations. It is an accessible resource for engineers, scientists, and applied mathematicians who seek more experience with theoretical or computational conformal mapping techniques. The most important theoretical results are stated and proved, but the emphasis throughout remains on concrete understanding and implementation, as evidenced by the 76 figures based on quantitatively correct illustrative examples. There are over 150 classical and modern reference works cited for readers needing more details. There is also a brief appendix illustrating the use of the Schwarz-Christoffel Toolbox for MATLAB, a package for computation of these maps.
Author: Sorin G. Gal
Publisher: Springer Science & Business Media
ISBN: 1461470986
Category : Mathematics
Languages : en
Pages : 206
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Book Description
This monograph deals with the quantitative overconvergence phenomenon in complex approximation by various operators. The book is divided into three chapters. First, the results for the Schurer-Faber operator, Beta operators of first kind, Bernstein-Durrmeyer-type operators and Lorentz operator are presented. The main focus is on results for several q-Bernstein kind of operators with q > 1, when the geometric order of approximation 1/qn is obtained not only in complex compact disks but also in quaternion compact disks and in other compact subsets of the complex plane. The focus then shifts to quantitative overconvergence and convolution overconvergence results for the complex potentials generated by the Beta and Gamma Euler's functions. Finally quantitative overconvergence results for the most classical orthogonal expansions (of Chebyshev, Legendre, Hermite, Laguerre and Gegenbauer kinds) attached to vector-valued functions are presented. Each chapter concludes with a notes and open problems section, thus providing stimulation for further research. An extensive bibliography and index complete the text. This book is suitable for researchers and graduate students working in complex approximation and its applications, mathematical analysis and numerical analysis.
