Group and a Class of Pseudodifferential Operators

Let H be the general, reduced Heisenberg group. Our main result establishes the inverse-closedness of a class of integral operators acting on Lp(H), given by the off-diagonal decay of the kernel. As a consequence of this result, we show that if α1δ + f , f ∈ L 1 v(H), is invertible with respect to convolution over H, then (α1δ + f) −1 = α2δ + g, g ∈ L 1 v(H). We prove analogous results for twisted convolution on a locally compact abelian group and its dual group. We apply the latter results to a class of Weyl pseudodifferential operators, and briefly discuss relevance to mobile communications.