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Recurrence Relations for Orthogonal Polynomials and Algebraicity of Solutions of the Dirichlet Problem

Chapter
Part of the International Mathematical Series book series (IMAT, volume 12)

Abstract

We show that any finite-term recurrence relation for planar orthogonal polynomials in a domain implies that the domain must be an ellipse. Our proof relies on Schwarz function techniques and on elementary properties of functions in Sobolev spaces.

Keywords

Dirichlet Problem Orthogonal Polynomial Recurrence Relation Connected Domain Polynomial Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of South FloridaTampaUSA
  2. 2.Department of Mathematics and StatisticsUniversity of CyprusNicosiaCyprus

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