Bergman orthogonal polynomials on an archipelago
Date
2008ISSN
1631-073XSource
Comptes Rendus MathematiqueVolume
346Issue
9-10Pages
499-502Google Scholar check
Metadata
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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.