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Domains of uniform convergence of real rational chebyshev approximants
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Ralitza K. Kovacheva
Published/Copyright:
July 29, 2016
Abstract
Let the function ƒ be real-valued and continuous on [-1,1]. Denote by Rn,n, n = 1,2, … the rational Chebyshev approximants of order (n,n) of f on the interval. The present paper is inspired by a conjecture raised up by A. A. Gonchar, namely: If all (starting with a number n0) rational functions Rn,n are analytic in some Joukowski’s ellipse Ɛ, then ƒ admits an analytic continuation from [-1,1] into Ɛ. We show that the hypothesis is true if the set of the free poles of Rn,n and the set of the alternation points are asymptotically “well distributed”.
Published Online: 2016-7-29
Published in Print: 2005-5-1
© 2016 Oldenbourg Wissenschaftsverlag GmbH, Rosenheimer Str. 145, 81671 München
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Keywords for this article
analytic continuation;
rational Chebyshev approximation;
alternation points
Articles in the same Issue
- Masthead
- A nonlinear-stability analysis of second-order fluid in porous medium in presence of magnetic field
- Convergence rate for some additive function on random permutations
- The converse of the Fabry-Pólya theorem on singularities of lacunary power series
- On meromorphic functions that share one value with their derivative
- Interrelations Between the Taylor Coefficients of a Matricial Carathéodory Function and Its Cayley Transform
- Domains of uniform convergence of real rational chebyshev approximants
- Regular statistical convergence of multiple sequences
