Sharp constants for rational approximations of analytic functions

A. I. Aptekarev

Sbornik. Mathematics, Tome 193 (2002) no. 1, pp. 1-72

Résumé

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.

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