论文标题
在约旦块案例中具有定期调制复发系数的正交多项式
Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case
论文作者
论文摘要
当$ 0 $位于相应的周期性雅各比矩阵的硬边缘时，我们研究具有定期调制复发系数的正交多项式。特别是，我们表明他们的正交度量绝对是绝对连续的，而在其补充上纯粹是离散的。此外，我们提供了根据Turán决定因素的密度的建设性公式。此外，我们确定正交多项式的确切渐近行为。最后，我们研究了ChristOffel-Darboux内核的缩放限制。
We study orthogonal polynomials with periodically modulated recurrence coefficients when $0$ lies on the hard edge of the spectrum of the corresponding periodic Jacobi matrix. In particular, we show that their orthogonality measure is purely absolutely continuous on a real half-line and purely discrete on its complement. Additionally, we provide the constructive formula for the density in terms of Turán determinants. Moreover, we determine the exact asymptotic behavior of the orthogonal polynomials. Finally, we study scaling limits of the Christoffel-Darboux kernel.
