Jordan块情形下具有周期调制递推系数的正交多项式

Jordan块情形下具有周期调制递推系数的正交多项式 II

Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case II

本文研究N周期调制Jacobi矩阵在转移矩阵收敛于Jordan块时的谱性质，刻画广义特征向量渐近行为，证明Turán行列式与Christoffel–Darboux核的收敛，并利用从属理论确定绝对连续谱和本质谱。

Asymptotic behaviour of Christoffel-Darboux kernel via three-term recurrence relation II

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.

Jordan algebras and orthogonal polynomials

We illustrate how Jordan algebras can provide a framework for the interpretation of certain classes of orthogonal polynomials. The big -1 Jacobi polynomials are eigenfunctions of a first order operator of Dunkl type. We consider an algebra that has this operator (up to constants) as one of its three generators and whose defining relations are given in terms of anticommutators. It is a special case of the Askey-Wilson algebra AW(3). We show how the structure and recurrence relations of the big -1 Jacobi polynomials are obtained from the representations of this algebra. We also present ladder op…

平面向量场中幂零特征方向上的高阶结构

Higher Order Structure along Nilpotent Eigendirections in Planar Vector Fields

本文研究线性化矩阵为非零二阶幂零矩阵的平面向量场的特殊一维限制，明确其性质、递推规律及抵消机制，并通过平面模型验证其与幂零正规形理论的互补性。

正交多项式无界递推系数的渐近零点分布

Asymptotic zeros' distribution of orthogonal polynomials with unbounded recurrence coefficients

研究无界递推系数雅可比矩阵有限截断的谱，通过分析Christoffel-Darboux核的渐进行为，推导正交多项式的强渐进行为，并证明特征值计数测度的Cauchy变换收敛。