Issues in Deconvolution, from Euclidean Space to the Heisenberg Group
by Wayne Eby  

Vol. 8 No. 3 (2013) P.323~P.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.

KEYWORDS
Pompeiu problem, Deconvolution, Heisenberg group, Laguerre functions, Bessel functions, Gelfand transform, Inversion

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 45E10, 45F05, 43A80

MILESTONES

Received: 2013-02-06
Revised : 2013-05-12
Accepted: 2013-05-13

Download Full Content