On the Distribution of Zeros and Poles of Rational Approximants on Intervals

V. V. Andrievskii, H.-P. Blatt and R. K. Kovacheva

Abstract and Applied Analysis, 2012, vol. 2012, 1-21

Abstract:

The distribution of zeros and poles of best rational approximants is well understood for the functions ð ‘“ ( ð ‘¥ ) = | ð ‘¥ | ð ›¼ , ð ›¼ > 0 . If ð ‘“ ∈ ð ¶ [ − 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, ð ‘Ž -values, and poles of best real rational approximants of degree at most ð ‘› to a function ð ‘“ ∈ ð ¶ [ − 1 , 1 ] that is real-valued, but not holomorphic on [ − 1 , 1 ] . Generalizations to the lower half of the Walsh table are indicated.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:961209

DOI: 10.1155/2012/961209

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