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

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


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.


Dirichlet Problem Orthogonal Polynomial Recurrence Relation Connected Domain Polynomial Solution 
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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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