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• W2951091059 abstract "In this paper we study the local zero behavior of orthogonal polynomials around an algebraic singularity, that is, when the measure of orthogonality is supported on $ [-1,1] $ and behaves like $ h(x)|x - x_0|^lambda dx $ for some $ x_0 in (-1,1) $, where $ h(x) $ is strictly positive and analytic. We shall sharpen the theorem of Yoram Last and Barry Simon and show that the so-called fine zero spacing (which is known for $ lambda = 0$) unravels in the general case, and the asymptotic behavior of neighbouring zeros around the singularity can be described with the zeros of the function $ c J_{frac{lambda - 1}{2}}(x) + d J_{frac{lambda + 1}{2}}(x) $, where $ J_a(x) $ denotes the Bessel function of the first kind and order $ a $. Moreover, using Sturm-Liouville theory, we study the behavior of this linear combination of Bessel functions, thus providing estimates for the zeros in question." @default.
• W2951091059 created "2019-06-27" @default.
• W2951091059 creator A5029041470 @default.
• W2951091059 creator A5036113611 @default.
• W2951091059 date "2016-10-24" @default.
• W2951091059 modified "2023-09-27" @default.
• W2951091059 title "Zeros of orthogonal polynomials near an algebraic singularity of the measure" @default.
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• W2951091059 hasPublicationYear "2016" @default.
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