Bergman Orthogonal Polynomials and the Grunsky Matrix

被引：0
作者：
Bernhard Beckermann
Nikos Stylianopoulos
机构：
[1] Univ. Lille,Laboratoire Painlevé UMR 8524 (AN
[2] University of Cyprus,EDP), UFR Mathématiques – M3
来源：
Constructive Approximation | 2018年 / 47卷
关键词：
Bergman orthogonal polynomials; Faber polynomials; Conformal mapping; Grunsky matrix; Bergman shift; Quasiconformal mapping; 30C10; 30C62; 41A10; 65E05; 30E10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
By exploiting a link between Bergman orthogonal polynomials and the Grunsky matrix, probably first observed by Kühnau (Ann Acad Sci Math 10:313–329, 1985), we improve on some recent results on strong asymptotics of Bergman polynomials outside the domain G of orthogonality, and on the entries of the Bergman shift operator. In our proofs, we suggest a new matrix approach involving the Grunsky matrix and use well-established results in the literature relating properties of the Grunsky matrix to the regularity of the boundary of G and the associated conformal maps. For quasiconformal boundaries, this approach allows for new insights for Bergman polynomials.
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页码：211 / 235
页数：24
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