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

Autor:	Ismail, Mourad E. H., Zhang, Ruiming, Zhou, Keru
Rok vydání:	2020
Předmět:	Mathematics - Classical Analysis and ODEs 33D45 33C45 47D03 26A33 41A36
Druh dokumentu:	Working Paper
Popis:	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. Comment: 31 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2012.07549 Zobrazit plný text záznamu View this record from Arxiv