Open Access
2012 On the Distribution of Zeros and Poles of Rational Approximants on Intervals
V. V. Andrievskii, H.-P. Blatt, R. K. Kovacheva
Abstr. Appl. Anal. 2012(SI13): 1-21 (2012). DOI: 10.1155/2012/961209


The distribution of zeros and poles of best rational approximants is well understood for the functions f(x)=|x|α, α>0. If fC[1,1] is not holomorphic on [1,1], the distribution of the zeros of best rational approximants is governed by the equilibrium measure of [1,1] under the additional assumption that the rational approximants are restricted to a bounded degree of the denominator. This phenomenon was discovered first for polynomial approximation. In this paper, we investigate the asymptotic distribution of zeros, respectively, a-values, and poles of best real rational approximants of degree at most n to a function fC[1,1] that is real-valued, but not holomorphic on [1,1]. Generalizations to the lower half of the Walsh table are indicated.


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V. V. Andrievskii. H.-P. Blatt. R. K. Kovacheva. "On the Distribution of Zeros and Poles of Rational Approximants on Intervals." Abstr. Appl. Anal. 2012 (SI13) 1 - 21, 2012.


Published: 2012
First available in Project Euclid: 5 April 2013

zbMATH: 1250.41005
MathSciNet: MR2947720
Digital Object Identifier: 10.1155/2012/961209

Rights: Copyright © 2012 Hindawi

Vol.2012 • No. SI13 • 2012
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