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 smoothness assumptions on the density. We
rely on our earlier work for the choice of the interpolation points, and dwell
on the Riemann-Hilbert approach to asymptotics of orthogonal polynomials
introduced by Kuijlaars, McLaughlin, Van Assche, and Vanlessen in the case of a
segment. We also elaborate on the ∂ˉ-extension of the
Riemann-Hilbert technique, initiated by McLaughlin and Miller on the line to
relax analyticity assumptions. This yields strong asymptotics for the
denominator polynomials of the multipoint Pade interpolants, from which
convergence follows.Comment: 42 pages, 3 figure
