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：

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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。