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Mat. Sb., 2002, Volume 193, Number 1, Pages 3–72 (Mi msb619)  

This article is cited in 53 scientific papers (total in 54 papers)

Sharp constants for rational approximations of analytic functions

A. I. Aptekarev

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences

Abstract: Theorems describing the sharp constants for the approximation of a general class of analytic functions by rational functions are proved. Magnus's conjecture on the sharp constant for the approximation of $e^{-z}$ on $[0,\infty]$ is established as a consequence. For the proof of the theorems new formulae expressing the strong asymptotics of polynomials orthogonal with respect to a varying complex weight are obtained.

DOI: https://doi.org/10.4213/sm619

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English version:
Sbornik: Mathematics, 2002, 193:1, 1–72

Bibliographic databases:

UDC: 517.53
MSC: 30E10, 41A20
Received: 12.03.2001

Citation: A. I. Aptekarev, “Sharp constants for rational approximations of analytic functions”, Mat. Sb., 193:1 (2002), 3–72; Sb. Math., 193:1 (2002), 1–72

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