Title

SPECTRAL PROPERTIES OF OPERATORS USING TRIDIAGONALIZATION

Authors

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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