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.

中文翻译：

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基于三项递归关系的Christoffel–Darboux核的渐近行为II

当0位于相应周期Jacobi矩阵的频谱的软边时，我们研究带有周期调制Jacobi参数的正交多项式。我们确定正交性度量何时绝对是连续的，并根据Turán行列式的极限为其提供建设性的公式。接下来，我们考虑相关联的二阶差分方程解的渐近性。最后，我们研究Christoffel–Darboux内核的缩放极限。