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.
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Dedicated to Professor Vladimir Maz’ya in recognition of his substantial contribution to the subject of Sobolev spaces
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Khavinson, D., Stylianopoulos, N. (2010). Recurrence Relations for Orthogonal Polynomials and Algebraicity of Solutions of the Dirichlet Problem. In: Laptev, A. (eds) Around the Research of Vladimir Maz'ya II. International Mathematical Series, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1343-2_9
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DOI: https://doi.org/10.1007/978-1-4419-1343-2_9
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