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arXiv · 2012.07549

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

Mourad E. H. Ismail·Ruiming Zhang·Keru Zhou
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Abstract

We introduce three one-parameter semigroups of operators and determine their spectra. Two of them 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.

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Mourad E. H. Ismail, Ruiming Zhang, Keru Zhou. 2020-12-11. q-Fractional Askey-Wilson Integrals and Related Semigroups of Operators. https://arxiv.org/abs/2012.07549

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