Harmonic analysis on some generalized Gelfand pairs attached to Heisenberg groups

摘要

Let H-n be the 2n + 1 -dimensional Heisenberg group. We consider the generalized Gelfand pairs (R* (sic) H-1, R*) and ((R-0 x SO(n)) (sic) R-0 x SO(n)) for n = 2. We describe the spherical distributions corresponding to these pairs and we obtain inversion formul ae in terms of them for the spaces of Schwartz functions on R-2n and H-n. We use the Tengstrand transform to compute the spherical distributions for n = 1 explicitly.