q-Fractional Askey-Wilson Integrals and Related Semigroups of Operators
Classical Analysis and ODEs
2020-12-15 v1
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.
Keywords
Cite
@article{arxiv.2012.07549,
title = {q-Fractional Askey-Wilson Integrals and Related Semigroups of Operators},
author = {Mourad E. H. Ismail and Ruiming Zhang and Keru Zhou},
journal= {arXiv preprint arXiv:2012.07549},
year = {2020}
}
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31 pages