Title

Spectral Properties Of Operators Using Tridiagonalization

Keywords

(q-)Askey scheme; Jacobi function transform; Jacobi polynomials; little (q-)Jacobi polynomials; spectral decomposition

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 AskeyWilson 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).-Jacobi function transform(q-) © 2012 World Scientific Publishing Company.

Publication Date

7-1-2012

Publication Title

Analysis and Applications

Volume

10

Issue

3

Number of Pages

327-343

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1142/S0219530512500157

Socpus ID

84866996886 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84866996886

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