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).
Des estimations de croissance pour la suite de polynômes orthogonaux se rapportant à la mesure d'aire sur une réunion finie de domaines de Jordan sont obtenues par une étude detaillée de la fonction de Green du complément et de la reflection de Schwarz dans les portions analytiques de la frontière. Deux applications en découlent : la distribution limite des zéros de la suite des polynômes orthogonaux de Bergman et un algorithme de reconstruction robuste de l'ouvert original à partir de données incomplètes (tomographiques par exemple).
Accepted:
Published online:
Björn Gustafsson 1; Mihai Putinar 2; Edward B. Saff 3; Nikos Stylianopoulos 4
@article{CRMATH_2008__346_9-10_499_0, author = {Bj\"orn Gustafsson and Mihai Putinar and Edward B. Saff and Nikos Stylianopoulos}, title = {Les polyn\^omes orthogonaux de {Bergman} sur un archipel}, journal = {Comptes Rendus. Math\'ematique}, pages = {499--502}, publisher = {Elsevier}, volume = {346}, number = {9-10}, year = {2008}, doi = {10.1016/j.crma.2008.03.001}, language = {fr}, }
TY - JOUR AU - Björn Gustafsson AU - Mihai Putinar AU - Edward B. Saff AU - Nikos Stylianopoulos TI - Les polynômes orthogonaux de Bergman sur un archipel JO - Comptes Rendus. Mathématique PY - 2008 SP - 499 EP - 502 VL - 346 IS - 9-10 PB - Elsevier DO - 10.1016/j.crma.2008.03.001 LA - fr ID - CRMATH_2008__346_9-10_499_0 ER -
Björn Gustafsson; Mihai Putinar; Edward B. Saff; Nikos Stylianopoulos. Les polynômes orthogonaux de Bergman sur un archipel. Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 499-502. doi : 10.1016/j.crma.2008.03.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.03.001/
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