Mathematical Physics Seminar

I will report on the results of my recent work with Dmitri Yafaev

(Rennes-1). We consider functions $\omega$ on the unit circle with a

finite number of logarithmic singularities. We study the approximation

of $\omega$ by rational functions in the BMO norm. We find the leading

term of the asymptotics of the distance in the BMO norm between

$\omega$ and the set of rational functions of degree $n$ as $n$ goes

to infinity. Our approach relies on the Adamyan-Arov-Krein theorem and

on the study of the asymptotic behaviour of singular values of Hankel

operators. In my talk, I will recall the background on approximation

theory and explain the connection with the theory of Hankel operators.