Section: New Results
Participant : Laurent Baratchart.
We studied this year the asymptotic behavior of the orthonormal polynomials with respect to a non-negative weight on a simply connected planar domain :
with the Kronecker symbol. We proved that if has boundary of class , , and if converges in some appropriate sense to a boundary function while not vanishing “too much” at the boundary, then
outside the convex hull of , with the conformal map from the complement of onto the complement of the unit disk normalized so that , and the so-called exterior Szegő function of .
This generalizes considerably known asymptotics on analytic domains with Hölder smooth non vanishing weights  . The proof rests on some Hardy space theory, conformal mapping and techniques. An exposition of the result was given at the conference Orthogonal and Multiple Orthogonal Polynomials, August 9-14 2015, Oaxaca (Mexico). An article is being written to report on this result.