q-fractional Askey–Wilson integrals and related semigroups of operators
Copyright policy )q-fractional Askey–Wilson integrals and related semigroups of operators
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.
31 pages
- Central South University China (People's Republic of)
- Guilin University of Electronic Technology China (People's Republic of)
- University of Central Florida United States
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), \(q\)-Hermite polynomials, Approximation by operators (in particular, by integral operators), inversion formulas, semigroups, Askey-Wilson operators, approximation operators, 33D45, 33C45, 47D03, 26A33, 41A36, Groups and semigroups of linear operators, Fractional derivatives and integrals, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, eigenvalues and eigenfunctions
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), \(q\)-Hermite polynomials, Approximation by operators (in particular, by integral operators), inversion formulas, semigroups, Askey-Wilson operators, approximation operators, 33D45, 33C45, 47D03, 26A33, 41A36, Groups and semigroups of linear operators, Fractional derivatives and integrals, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, eigenvalues and eigenfunctions
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