Best rational approximation of functions with logarithmic singularities
Pushnitski, Alexander · Yafaev, Dmitri
Original · EN
We consider functions ω on the unit circle 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→∞. 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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