Spectral decomposition and matrix-valued orthogonal polynomials

    Authors

    W. Groenevelt; M. E. H. Ismail;E. Koelink

    Comments

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    Abbreviated Journal Title

    Adv. Math.

    Keywords

    Matrix-valued orthogonal polynomials; Spectral theory; ASKEY-WILSON POLYNOMIALS; SPHERICAL-FUNCTIONS; SU(2); Mathematics

    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 x 2-matrix-valued analogues of subfamilies of Askey-Wilson polynomials. (C) 2013 Elsevier Inc. All rights reserved.

    Journal Title

    Advances in Mathematics

    Volume

    244

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    91

    Last Page

    105

    WOS Identifier

    WOS:000322423500005

    ISSN

    0001-8708

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