A connection between orthogonal polynomials on the unit circle and matrix orthogonal polynomials on the real line
Abstract
Szego's procedure to connect orthogonal polynomials on the unit circle and orthogonal polynomials on [-1,1] is generalized to nonsymmetric measures. It generates the so-called semi-orthogonal functions on the linear space of Laurent polynomials L, and leads to a new orthogonality structure in the module LxL. This structure can be interpreted in terms of a 2x2 matrix measure on [-1,1], and semi-orthogonal functions provide the corresponding sequence of orthogonal matrix polynomials. This gives a connection between orthogonal polynomials on the unit circle and certain classes of matrix orthogonal polynomials on [-1,1]. As an application, the strong asymptotics of these matrix orthogonal polynomials is derived, obtaining an explicit expression for the corresponding Szego's matrix function.
Cite
@article{arxiv.math/0204294,
title = {A connection between orthogonal polynomials on the unit circle and matrix orthogonal polynomials on the real line},
author = {Maria J. Cantero and Maria P. Ferrer and Leandro Moral and Luis Velazquez},
journal= {arXiv preprint arXiv:math/0204294},
year = {2015}
}
Comments
28 pages