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Session S32 - Special functions and orthogonal polynomials

Monday, July 12, 14:00 ~ 15:00 UTC-3

$q$-Fractional Askey--Wilson Integrals and Related Semigroups of Operators

Mourad Ismail

University of Central Florida, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We introduce three one parameter semigroups of operators and determine their spectra. They are fractional integrals associated with the Askey--Wilson operator. We also study these families as families of positive linear approximation operators. Applications include connection relations and bilinear formulas for the Askey--Wilson polynomials. We also introduce a $q$-Gauss--Weierstrass transform and prove a representation and inversion theorem for it.

Joint work with Ruiming Zhang and Keru Zhou..

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