Now showing items 11-20 of 36
Matrix valued orthogonal polynomials satisfying differential equations [Presentation]
The theory of matrix valued orthogonal polynomials goes back to the fundamental works of M. G. Krein. If one is considering possible applications of these polynomials, it is natural to concentrate on those cases where some ...
Non-commutative Painlevé equations and Hermite-type matrix orthogonal polynomials [Article]
We study double integral representations of Christoffel-Darboux kernels associated with two examples of Hermite-type matrix orthogonal polynomials. We show that the Fredholm determinants connected with these kernels are ...
Principal dynamical components [Article]
A new procedure is proposed for the dimensional reduction of time series. Similarly to principal components, the procedure seeks a low-dimensional manifold that minimizes information loss. Unlike principal components, ...
Some examples of matrix-valued orthogonal functions having a differential and an integral operator as eigenfunctions [Article]
The aim of this paper is to show some examples of matrix-valued orthogonal functions on the real line which are simultaneously eigenfunctions of a second-order differential operator of Schrödinger type and an integral ...
Matrix valued orthogonal polynomials arising from group representation theory and a family of quasi-birth-and-death processes [Article]
(Society for Industrial and Applied Mathematics, 2008)
We consider a family of matrix valued orthogonal polynomials obtained by Pacharoni and Tirao in connection with spherical functions for the pair (SU(N + 1), U(N)); see [I. Pacharoni and J. A. Tirao, Constr. Approx., 25 ...
Propiedades diferenciales de familias de polinomios ortogonales matriciales y aplicaciones [PhD Thesis]
Una de las vías más fructíferas de aplicación de la teoría de polinomios ortogonales se produce a través de las ecuaciones diferenciales de segundo orden satisfechas por las familias clásicas de Hermite, Laguerre y Jacobi. ...