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Titchmarsh–Weyl Formula for the Spectral Density of a Class of Jacobi Matrices in the Critical Case
Functional Analysis and Its Applications ( IF 0.6 ) Pub Date : 2021-11-08 , DOI: 10.1134/s0016266321020027
S. N. Naboko 1 , S. A. Simonov 1, 2
Affiliation  

Abstract

We consider a class of Jacobi matrices with unbounded entries in the so-called critical (double root, Jordan block) case. We prove a formula which relates the spectral density of a matrix to the asymptotics of orthogonal polynomials associated with it.



中文翻译:

临界情况下一类 Jacobi 矩阵的谱密度的 Titchmarsh-Weyl 公式

摘要

我们在所谓的临界(双根,Jordan 块)情况下考虑一类具有无限项的雅可比矩阵。我们证明了一个公式,该公式将矩阵的谱密度与与之相关的正交多项式的渐近线联系起来。

更新日期:2021-11-09
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