Work

Spectral decomposition and matrix-valued orthogonal polynomials

Year: 2012

Type: preprint

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

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1206.4785

Authors: Groenevelt, Wolter, Ismail, Mourad E. H., Koelink, Erik

Institutions: Delft University of Technology, University of Central Florida, King Saud University, Radboud University Nijmegen

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: King Saud University, National Plan for Science, Technology and Innovation

Award: G4560259130

OpenAlex ID: W2953021233

Cites: 13

Cited by:

Related to: 20