Bergman orthogonal polynomials on an archipelago

Abstract

Growth estimates for orthogonal polynomials with respect to area measure (Bergman polynomials) over the union of finitely many Jordan regions with piecewise smooth boundary are obtained by a careful investigation of the Green function of the complement, and of Schwarz reflection in analytic arcs of the boundary. As applications we obtain a detailed picture of the limiting zero distribution of Bergman's orthogonal polynomials, and also we propose a robust reconstruction algorithm of the original open set, starting from incomplete data (such as obtained by geometric tomography). To cite this article: B. Gustafsson et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008). © 2008 Académie des sciences.