Inverse-Closedness of a Banach Algebra of Integral Operators on the Heisenberg Group
| dc.creator | Farrell, Brendan | |
| dc.creator | Strohmer, Thomas | |
| dc.date | 2006-12-01 | |
| dc.date | 2007-12-06 | |
| dc.date.accessioned | 2026-07-07T08:47:34Z | |
| dc.date.available | 2026-07-07T08:47:34Z | |
| dc.description | Let $\mathbb{H}$ be the general, reduced Heisenberg group. Our main result establishes the inverse-closedness of a class of integral operators acting on $L^{p}(\mathbb{H})$, given by the off-diagonal decay of the kernel. As a consequence of this result, we show that if $α_{1}I+S_{f}$, where $S_{f}$ is the operator given by convolution with $f$, $f\in L^{1}_{v}(\mathbb{H})$, is invertible in $\B(L^{p}(\mathbb{H}))$, then (α_{1}I+S_{f})^{-1}=α_{2}I+S_{g}$, and $g\in L^{1}_{v}(\mathbb{H})$. 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. | |
| dc.description | This version corrects two mistakes and recognizes the work of other authors related to a corollary of our main theorem | |
| dc.identifier | https://arxiv.org/abs/math/0612033 | |
| dc.identifier | http://arxiv.org/abs/math/0612033 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143644 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 43A20; 47G30 | |
| dc.title | Inverse-Closedness of a Banach Algebra of Integral Operators on the Heisenberg Group | |
| dc.type | text |