Best rational approximation of functions with logarithmic singularities

We consider functions $ω$ on the unit circle $\mathbb T$ with a finite number of logarithmic singularities. We study the approximation of $ω$ by rational functions and find an asymptotic formula for the distance in the BMO-norm between $ω$ 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.

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