On finite-term recurrence relations for Bergman and Szego{double acute} polynomials
Date
2012ISSN
1617-9447Source
Computational Methods and Function TheoryVolume
12Issue
2Pages
393-402Google Scholar check
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With the aid of Havin's Lemma (which we generalize) we prove that polynomials orthogonal over the unit disk with respect to certain weighted area measures (Bergman polynomials) cannot satisfy a finite-term recurrence relation unless the weight is radial, in which case the polynomials are simply monomials. For polynomials orthogonal over the unit circle (Szego{double acute} polynomials) we provide a simple argument to show that the existence of a finite-term recurrence implies that the weight must be the reciprocal of the square modulus of a polynomial. © 2012 Heldermann Verlag.