Finite-Term Relations for Planar Orthogonal Polynomials

被引：0
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作者：
Mihai Putinar
Nikos S. Stylianopoulos
机构：
[1] University of California at Santa Barbara,Department of Mathematics
[2] University of Cyprus,Department of Mathematics and Statistics
来源：
Complex Analysis and Operator Theory | 2007年 / 1卷
关键词：
Primary 30C10; Secondary 47B32, 30C40, 31A25; Orthogonal polynomials; algebraic curves; Dirichlet’s problem; Bergman space;
D O I：
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学科分类号：
摘要：
We prove by elementary means that, if the Bergman orthogonal polynomials of a bounded simply-connected planar domain, with sufficiently regular boundary, satisfy a finite-term relation, then the domain is algebraic and characterized by the fact that Dirichlet’s problem with boundary polynomial data has a polynomial solution. This, and an additional compactness assumption, is known to imply that the domain is an ellipse. In particular, we show that if the Bergman orthogonal polynomials satisfy a three-term relation then the domain is an ellipse. This completes an inquiry started forty years ago by Peter Duren.
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页码：447 / 456
页数：9
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