2013 / September Volume 8 No.3
Issues in Deconvolution, from Euclidean Space to the Heisenberg Group
| Published Date |
2013 / September
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|---|---|
| Title | Issues in Deconvolution, from Euclidean Space to the Heisenberg Group |
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| Pagination | 323-350 |
| Abstract | We review some of the important results on deconvolution, particularly the multi-channel deconvolution problem, for the setting of Euclidean space, focusing on the central role of the Hormander strongly coprime condition in this area of analysis. We then address the problem of deconvolution in the Heisenberg group setting, beginning with the results of [16]. We also extend the results of [16] to three solid tori, a higher dimensional analogue of the three squares considered in [9]. The work of [16] on multi-channel deconvolution is ongoing research, with several important issues still to be fully explored. We address some of these issues, with particular attention to extension of the strongly coprime condition. We also recall the related result of [16] providing a means to extend a deconvolution from a complex space to the Heisenberg group setting and consider a few extensions of this result.
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| AMS Subject Classification |
45E10, 45F05, 43A80
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| Received |
2013-05-12
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| Accepted |
2013-05-13
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