Whittaker transform on distributions

Abstract

The aim of this paper is to construct a testing function space equipped with the topology generated by the L_{v,p}-multinorm of the differential operator Bx = -4x^2 d^2/dx^2- 1 + x^2 -ux, where u < 1/2, v>0, p in [1, \infinity[, and its k-iterates B^k_x where k = 0, 1,..., and B^0_x \phi=\phi. We also introduce the correspondent dual space for the index Whittaker transform on distributions. The existence, uniqueness, imbedding and inversion properties are investigated.