The poles of Tchebycheff rational approximations and meromorphic extension of functions

V. A. Prokhorov

Belarusian State University

Abstract: A characterization is given for an $m$-meromorphic continuation of a continuous function $f$ on the segment $[-1,1]$, in terms of the asymptotic behavior of the finite poles of the $m$th row of the table of Tchebycheff rational approximants to $f$.

UDC: 517.53

MSC: Primary 30D30; Secondary 30E10

Received: 05.10.1988 and 19.10.1989

 English version: Mathematics of the USSR-Sbornik, 1991, 69:2, 379–391

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