6 papers
Spectral theory and special functions
Erik Koelink
A short introduction to the use of the spectral theorem for self-adjoint operators in the theory of special functions is given. As the first example, the spectral theorem is applie…
Transmutation kernels for the little q-Jacobi function transform
Erik Koelink, Hjalmar Rosengren
The little q-Jacobi function transform depends on three parameters. An explicit expression as a sum of two very-well-poised 8W7-series is derived for the dual transmutation kernel…
Harmonic analysis on the SU(2) dynamical quantum group
Erik Koelink, Hjalmar Rosengren
Dynamical quantum groups were recently introduced by Etingof and Varchenko as an algebraic framework for studying the dynamical Yang-Baxter equation, which is precisely the Yang-Ba…
The Askey-Wilson function transform scheme
Erik Koelink, Jasper V. Stokman
In this paper we present an addition to Askey's scheme of q-hypergeometric orthogonal polynomials involving classes of q-special functions which do not consist of polynomials only.…
The big q-Jacobi function transform
Erik Koelink, Jasper V. Stokman
We give a detailed description of the resolution of the identity of a second order -difference operator considered as an unbounded self-adjoint operator on two different Hilbert…
q-Laguerre polynomials and big q-Bessel functions and their orthogonality relations
Nicola Ciccoli, Erik Koelink, Tom H. Koornwinder
The q-Laguerre polynomials correspond to an indetermined moment problem. For explicit discrete non-N-extremal measures corresponding to Ramanujan's -summation we complemen…