The vector-valued big q-Jacobi transform

Abstract

Big $q$-Jacobi functions are eigenfunctions of a second order $q$-difference operator $L$. We study $L$ as an unbounded self-adjoint operator on an $L^2$-space of functions on $\mathbb{R}$ with a discrete measure. We describe explicitly the spectral decomposition of $L$ using an integral transform $\mathcal{F}$ with two different big $q$-Jacobi functions as a kernel, and we construct the inverse of $\mathcal{F}$.

35 pages, corrected an error and typos

References in corpus (1)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue