## View abstract

### 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

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.