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

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 $\{q^k,k=0,1,2,3,\dots \}$, 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.

24 pages, 5 figures

Cited by in corpus (2)

• On a class of q-orthogonal polynomials and the q-Riemann Hilbert Problem
• Asymptotic behaviours of q-orthogonal polynomials from a q-Riemann Hilbert Problem