2020/12/11 by Mourad E. H. Ismail, Ismail, Mourad E. H., Ruiming Zhang +3
Mathematics · #26A33 #33C45 #33D45 #41A36 #47D03 #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.2012.07549
openalex publication_date 2020/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.