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arXiv · 1910.12518

Zero distribution of orthogonal polynomials on a $q$-lattice

Walter Van Assche·Quinten Van Baelen
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Abstract

We give the asymptotic behavior of the zeros of orthogonal polynomials, after appropriate scaling, for which the orthogonality measure is supported on the $q$-lattice $\{q^k, k=0,1,2,3,\ldots\}$, where $0 < q < 1$. The asymptotic distribution of the zeros is given by the radial part of the equilibrium measure of an extremal problem in logarithmic potential theory for circular symmetric measures with a constraint imposed by the $q$-lattice.

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Walter Van Assche, Quinten Van Baelen. 2019-10-28. Zero distribution of orthogonal polynomials on a $q$-lattice. https://doi.org/10.1007/s00365-020-09513-2

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