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Article Dans Une Revue Constructive Approximation Année : 2017

Best rational approximation of functions with logarithmic singularities

Résumé

We consider functions $\omega$ on the unit circle $\mathbb T$ with a finite number of logarithmic singularities. We study the approximation of $\omega$ by rational functions and find an asymptotic formula for the distance in the BMO-norm between $\omega$ and the set of rational functions of degree $n$ as $n\to\infty$. Our approach relies on the Adamyan-Arov-Krein theorem and on the study of the asymptotic behaviour of singular values of Hankel operators.

Dates et versions

hal-01342776 , version 1 (06-07-2016)

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Alexander Pushnitski, Dimitri R Yafaev. Best rational approximation of functions with logarithmic singularities. Constructive Approximation, 2017, 46 (2), pp.243-269. ⟨10.1007/s00365-016-9347-1⟩. ⟨hal-01342776⟩
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