English

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 2×22\times 2-matrix-valued analogues of subfamilies of Askey-Wilson polynomials.

Keywords

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

R2 v1 2026-06-21T21:23:07.950Z