Baricz, Á. & Danka, T. (2018) Constructive Approximation [Matematică, Q1]

Publicat: 24 Noiembrie 2020

Baricz, Á. & Danka, T. (2018) Zeros of orthogonal polynomials near an algebraic singularity of the measure. Constructive Approximation, 47(3), 407-435.

DOI: https://doi.org/10.1007/s00365-017-9411-5

✓ Publisher: Springer
✓ Web of Science Core Collection: Science Citation Index Expanded
✓ Categories: Mathematics
✓ Article Influence Score (AIS): 1.29 (2018) / Q1

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 and behaves like for some , 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 ) unravels in the general case, and the asymptotic behavior of neighbouring zeros around the singularity can be described with the zeros of the function , where 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.

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