This survey paper summarizes the more important recent applications of the eigenpairs
formulas for a family of tridiagonal matrices based on Losonczi's seminal work of almost …

This computationally oriented book describes and explains the mathematical relationships
among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and …

The purpose of this article is to derive a class of multi-soliton solutions of the Burgers
equation employing Darboux transformation with the help of the Lax pair. By means of an …

The Christoffel-Darboux kernel, a central object in approximation theory, is shown to have
many potential uses in modern data analysis, including applications in machine learning …

Given a matrix polynomial, matrix bi-orthogonal polynomials with respect to the sesquilinear
form where is a matrix of Borel measures supported in some infinite subset of the real line …

We consider the most general Dunkl shift operator L with the following properties:(i) L is of
first order in the shift operator and involves reflections;(ii) L preserves the space of …

In this paper we state and prove some properties of the zeros of exceptional Jacobi and
Laguerre polynomials. Generically, the zeros of exceptional polynomials fall into two …

The wave-operator nonlinear Schrödinger equation was introduced in the literature. Further,
nonlocal space–time reverse complex field equations were also recently introduced. Studies …

Abstract Using Casorati determinants of Hahn polynomials (hn α, β, N) n, we construct for
each pair F=(F 1, F 2) of finite sets of positive integers polynomials hn α, β, N; F, n∈ σ F …

In this paper, Geronimus transformations for matrix orthogonal polynomials in the real line
are studied. The orthogonality is understood in a broad sense, and is given in terms of a …