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arXiv · 1810.00564

Weak limits of the measures of maximal entropy for Orthogonal polynomials

Carsten Lunde Petersen·Eva Uhre
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Abstract

In this paper we study the sequence of orthonormal polynomials $\{P_n(μ; z)\}$ defined by a probability measure $μ$ with non-polar compact support $S(μ)\subset\mathbb C$. We show that the support of any weak* limit of the sequence of measures of maximal entropy $ω_n$ for $P_n$ is contained in the polynomial-convex hull of $S(μ)$. And for $n$-th root regular measures the $ω_n$ converge weak* to the equilibrium measure on $S(μ)$.

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Carsten Lunde Petersen, Eva Uhre. 2020-01-28. Weak limits of the measures of maximal entropy for Orthogonal polynomials. https://doi.org/10.1007/s11118-019-09824-5

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