SPECTRAL PROPERTIES OF OPERATORS USING TRIDIAGONALIZATION

    Authors

    M. E. H. Ismail;E. Koelink

    Comments

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    Abbreviated Journal Title

    Anal. Appl.

    Keywords

    Jacobi function transform; (q-)Askey scheme; Jacobi polynomials; little; (q-)Jacobi polynomials; spectral decomposition; J-MATRIX METHOD; POLYNOMIALS; TRANSFORM; CONTINUUM; Mathematics, Applied; Mathematics

    Abstract

    A general scheme for tridiagonalizing differential, difference or q-difference operators using orthogonal polynomials is described. From the tridiagonal form the spectral decomposition can be described in terms of the orthogonality measure of generally different orthogonal polynomials. Three examples are worked out: (1) related to Jacobi and Wilson polynomials for a second order differential operator, (2) related to little q-Jacobi polynomials and Askey-Wilson polynomials for a bounded second order q-difference operator, (3) related to little q-Jacobi polynomials for an unbounded second order q-difference operator. In case (1) a link with the Jacobi function transform is established, for which we give a q-analogue using example (2).

    Journal Title

    Analysis and Applications

    Volume

    10

    Issue/Number

    3

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    327

    Last Page

    343

    WOS Identifier

    WOS:000306329100005

    ISSN

    0219-5305

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