论文标题
克里斯托佛尔 - 达布克斯内核的渐近行为通过三项复发关系ii ii
Asymptotic behaviour of Christoffel-Darboux kernel via three-term recurrence relation II
论文作者
论文摘要
我们研究具有定期调制的Jacobi参数的正交多项式，当时$ 0 $位于相应的周期性雅各比矩阵的柔软边缘。我们确定何时完全连续的正交性度量，并根据Turán决定因素的极限为其提供建设性公式。接下来，我们考虑相关的二阶差异方程解决方案的渐近学。最后，我们研究了Christoffel的缩放限制 - Darboux内核。
We study orthogonal polynomials with periodically modulated Jacobi parameters in the case when $0$ lies on the soft edge of the spectrum of the corresponding periodic Jacobi matrix. We determine when the orthogonality measure is absolutely continuous and we provide a constructive formula for it in terms of the limit of Turán determinants. We next consider asymptotics of the solutions of associated second order difference equation. Finally, we study scaling limits of the Christoffel--Darboux kernel.
