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We consider multipoint Pad e approximation to Cauchy transforms of com- plex measures. We show that if the support of a measure is an analytic Jordan arc and if the measure itself is absolutely continuous with respect to the equilibrium distribution of that arc with Dini-smooth non-vanishing density, then the diagonal multipoint Pad e approximants associated with appropriate interpolation schemes converge locally uniformly to the approximated Cauchy transform in the comple- ment of the arc. This asymptotic behavior of Pad e approximants is deduced from the analysis of underlying non-Hermitian orthogonal polynomials, for which we use classical properties of Hankel and Toeplitz operators on smooth curves. A construc- tion of the appropriate interpolation schemes is explicit granted the parametrization of the arc.

Convergent Interpolation to Cauchy Integrals over Analytic Arcs