Bergman orthogonal polynomials on an archipelago

• 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).

Nyckelord

planar domains

approximation

Publikations- och innehållstyp

ref (ämneskategori)

art (ämneskategori)