The vector-valued big q-Jacobi transform

الأصل · EN

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 L²-space of functions on R with a discrete measure. We describe explicitly the spectral decomposition of L using an integral transform F with two different big q-Jacobi functions as a kernel, and we construct the inverse of F.