33 citations · 85 across the 28 of their papers we have counts for
10 papers · 1 filter
Lower bounds in -rational approximation to Blaschke products
Laurent Baratchart, Alexander Borichev, Sylvain Chevillard +2
We derive lower bounds in best rational approximation of given degree to finite Blaschke products, in the Hardy space of the unit disk. We first consider approximation to $z^…
Padé approximants to certain elliptic-type functions
Laurent Baratchart, Maxim Yattselev
Given non-collinear points a_1, a_2, a_3, there is a unique compact, say Δ, that has minimal logarithmic capacity among all continua joining a_1, a_2, and a_3. For h be a complex-v…
Weighted Extremal Domains and Best Rational Approximation
Laurent Baratchart, Herbert Stahl, Maxim Yattselev
Let f be holomorphically continuable over the complex plane except for finitely many branch points contained in the unit disk. We prove that best rational approximants to f of degr…
Asymptotics of Padé approximants to a certain class of elliptic-type functions
Laurent Baratchart, Maxim Yattselev
In this paper we investigate the question of uniform convergence of Padé approximants to elliptic functions that can be represented as Cauchy integrals of Dini-continuous non-vanis…
Convergent Interpolation to Cauchy Integrals over Analytic Arcs with Jacobi-Type Weights
Laurent Baratchart, Maxim Yattselev
We design convergent multipoint Pade interpolation schemes to Cauchy transforms of non-vanishing complex densities with respect to Jacobi-type weights on analytic arcs, under mild…
Asymptotic Uniqueness of Best Rational Approximants to Complex Cauchy Transforms in of the Circle
Laurent Baratchart, Maxim Yattselev
For all n large enough, we show uniqueness of a critical point in best rational approximation of degree n, in the L^2-sense on the unit circle, to functions f, where f is a sum of…