A New Approach to Ratio Asymptotics for Orthogonal Polynomials

A set of orthogonal polynomials, dual to alternative q-Charlier polynomials

The aim of this paper is to derive (by using two operators, representable by a Jacobi matrix) a family of q-orthogonal polynomials, which turn to be dual to alternative q-Charlier polynomials. A discrete orthogonality relation and a three-term recurrence relation for these dual polynomials are explicitly obtained. The completeness property of dual alternative q-Charlier polynomials is also established.

The Analytic Theory of Matrix Orthogonal Polynomials

We give a survey of the analytic theory of matrix orthogonal polynomials.

Spectral decomposition and matrix-valued orthogonal polynomials

The relation between the spectral decomposition of a self-adjoint operator which is realizable as a higher order recurrence operator and matrix-valued orthogonal polynomials is investigated. A general construction of such operators from scalar-valued orthogonal polynomials is presented. Two examples of matrix-valued orthogonal polynomials with explicit orthogonality relations and three-term recurrence relation are presented, which both can be considered as $2\times 2$-matrix-valued analogues of subfamilies of Askey-Wilson polynomials.

Recovering orthogonality from Quasi-type Kernel Polynomials using specific spectral transformations

In this work, the concept of quasi-type Kernel polynomials with respect to a moment functional is introduced. Difference equation satisfied by these polynomials along with the criterion for orthogonality conditions are discussed. The process of recovering orthogonality for the linear combination of a quasi-type kernel polynomial with another orthogonal polynomial, which is identified by involving linear spectral transformation, is provided. This process involves an expression of ratio of iterated kernel polynomials. This lead to considering the limiting case of ratio of kernel polynomials invo…

多重正交多项式零点：位置与交错

Zeros of Multiple Orthogonal Polynomials: Location and Interlacing

本文通过Christoffel变换的正常性准则，研究了多重正交多项式零点的位置和交错特性，并验证了其在Nikishin和Angelsco系统中的应用。

Orthogonal polynomials on the unit circle: New results

We announce numerous new results in the theory of orthogonal polynomials on the unit circle.