Bibliographic Details
| Title: |
Zero sets, entropy, and pointwise asymptotics of orthogonal polynomials. |
| Authors: |
Bessonov, Roman1,2 (AUTHOR) bessonov@pdmi.ras.ru, Denisov, Sergey1,3,4 (AUTHOR) denissov@wisc.edu |
| Source: |
Journal of Functional Analysis. Jun2021, Vol. 280 Issue 12, pN.PAG-N.PAG. 1p. |
| Subjects: |
Schur functions, Generating functions, Entropy, Orthogonal polynomials, Polynomials, Oscillations |
| Abstract: |
Let μ be a measure from Szegő class on the unit circle T and let { f n } be the family of Schur functions generated by μ. In this paper, we prove a version of the classical Szegő's formula, which controls the oscillation of f n on T for all n ⩾ 0. Then, we focus on an analog of Lusin's conjecture for polynomials { φ n } orthogonal with respect to measure μ and prove that pointwise convergence of { | φ n | } almost everywhere on T is equivalent to a certain condition on zeroes of φ n. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
