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3 - Applications of Spectral Theory to Special Functions

Published online by Cambridge University Press:  07 October 2020

By
Erik Koelink
Edited by
Howard S. Cohl  and
Mourad E. H. Ismail
Howard S. Cohl
Affiliation:
National Institute of Standards and Technology
Mourad E. H. Ismail
Affiliation:
University of Central Florida
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Summary

Many special functions are eigenfunctions to explicit operators, such as difference and differential operators, which is in particular true for the special functions occurring in the Askey scheme, its q-analogue and extensions. The study of the spectral properties of such operators leads to explicit information for the corresponding special functions. We discuss several instances of this application, involving orthogonal polynomials and their matrix-valued analogues.

Keywords

special functionsspectral theoryAskey schemedifference operatorsdifferential operatorsJacobi operatorsmatrix-valued orthogonal polynomialsJ-matrix methodspectral theorem
Type
Chapter
Information
Lectures on Orthogonal Polynomials and Special Functions , pp. 131 - 212
Publisher: Cambridge University Press
Print publication year: 2020

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