Best Rational Approximation of Functions with Logarithmic Singularities
Alexander Pushnitski - Personal Name
Dmitri Yafaev - Personal Name
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.
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.
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Hankel operators
Asymptotics of singular values
Logarithmic singularities
Rational approximation
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