Inverse-Closedness of a Banach Algebra of Integral Operators on the Heisenberg Group
نویسندگان
چکیده
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 ∈ Lv(H), is invertible in B(Lp(H)), then (α1I + Sf )−1 = α2I + Sg, and g ∈ Lv(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.
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