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 behavior of singular values
of Hankel operators.

• Best Rational Approximation of Functions with Logarithmic Singularities