Uncertainty principles on certain Lie groups View Full Text


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Article Info

DATE

1995-05

AUTHORS

A Sitaram, M Sundari, S Thangavelu

ABSTRACT

There are several ways of formulating the uncertainty principle for the Fourier transform on ℝn. Roughly speaking, the uncertainty principle says that if a functionf is ‘concentrated’ then its Fourier transform cannot be ‘concentrated’ unlessf 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 groups and the Euclidean motion group of the plane. More... »

PAGES

135-151

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf02880360

DOI

http://dx.doi.org/10.1007/bf02880360

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1010789907


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