Spectral decomposition and matrix-valued orthogonal polynomials
Classical Analysis and ODEs
2014-03-13 v1 Spectral Theory
Abstract
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 -matrix-valued analogues of subfamilies of Askey-Wilson polynomials.
Cite
@article{arxiv.1206.4785,
title = {Spectral decomposition and matrix-valued orthogonal polynomials},
author = {Wolter Groenevelt and Mourad E. H. Ismail and Erik Koelink},
journal= {arXiv preprint arXiv:1206.4785},
year = {2014}
}
Comments
15 pages