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Walsh Equiconvergence of Complex Interpolating Polynomials [electronic resource] /by Amnon Jakimovski, Ambikeshwar Sharma, József Szabados.

by Jakimovski, Amnon [author.]; Sharma, Ambikeshwar [author.]; Szabados, József [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Springer Monographs in Mathematics: Publisher: Dordrecht : Springer Netherlands, 2006.Description: XIII, 296 p. online resource.ISBN: 9781402041754.Subject(s): Mathematics | Global analysis (Mathematics) | Functions of complex variables | Sequences (Mathematics) | Differential equations, partial | Mathematics | Approximations and Expansions | Analysis | Functions of a Complex Variable | Sequences, Series, Summability | Several Complex Variables and Analytic SpacesDDC classification: 511.4 Online resources: Click here to access online
Contents:
Lagrange Interpolation and Walsh Equiconvergence -- Hermite and Hermite-Birkhoff Interpolation and Walsh Equiconvergence -- A Generalization of the Taylor Series to Rational Functions and Walsh Equiconvergence -- Sharpness Results -- Converse Results -- Padé Approximation and Walsh Equiconvergence for Meromorphic Functions with ?–Poles -- Quantitative Results in the Equiconvergence of Approximation of Meromorphic Functions -- Equiconvergence for Functions Analytic in an Ellipse -- Walsh Equiconvergence Theorems for the Faber Series -- Equiconvergence on Lemniscates -- Walsh Equiconvergence and Equisummability.
In: Springer eBooksSummary: 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.
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Lagrange Interpolation and Walsh Equiconvergence -- Hermite and Hermite-Birkhoff Interpolation and Walsh Equiconvergence -- A Generalization of the Taylor Series to Rational Functions and Walsh Equiconvergence -- Sharpness Results -- Converse Results -- Padé Approximation and Walsh Equiconvergence for Meromorphic Functions with ?–Poles -- Quantitative Results in the Equiconvergence of Approximation of Meromorphic Functions -- Equiconvergence for Functions Analytic in an Ellipse -- Walsh Equiconvergence Theorems for the Faber Series -- Equiconvergence on Lemniscates -- Walsh Equiconvergence and Equisummability.

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.

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