Inverse-Closedness of a Banach Algebra of Integral Operators on the Heisenberg Group

الأصل · EN

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 α₁I+Sf, where Sf is the operator given by convolution with f, f∈ L¹ᵥ(H), is invertible in (Lᵖ(H)), then (α₁I+Sf)⁻¹=α₂I+Sg, and g∈ L¹ᵥ(H). We prove analogous results for twisted convolution operators and apply the latter results to a class of Weyl pseudodifferential operators. We briefly discuss relevance to mobile communications.