Uncertainty principles on certain Lie groups

Sitaram, A. ; Sundari, M. ; Thangavelu, S. (1995) Uncertainty principles on certain Lie groups Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 105 (2). pp. 135-151. ISSN 0253-4142

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Official URL: http://www.ias.ac.in/j_archive/mathsci/105/2/135-1...

Related URL: http://dx.doi.org/10.1007/BF02880360


There are several ways of formulating the uncertainty principle for the Fourier transform on Rn. Roughly speaking, the uncertainty principle says that if a function f is 'concentrated' then its Fourier transform f~ cannot be 'concentrated' unless f is identically zero. Of course, in the above, we should be precise about what we mean by 'concentration'. There are several ways of measuring 'concentration' and depending on the definition we get a host of uncertainty principles. As several authors have shown, some of these uncertainty principles seem to be a general feature of harmonic analysis on connected locally compact groups. In this paper, we show how various uncertainty principles take form in the case of some locally compact groups including Rn, the Heisenberg group, the reduced Heisenberg group and the Euclidean motion group of the plane.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Fourier Transform; Heisenberg Group; Motion Group; Uncertainty Principle
ID Code:64417
Deposited On:10 Oct 2011 05:51
Last Modified:18 May 2016 12:51

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