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A qualitative uncertainty principle for semisimple Lie groups

Part of: Lie groups Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

Michael Cowling ,
John F. Price  and
Alladi Sitaram
Michael Cowling
Affiliation:
School of MathematicsUniversity of New South WalesKensington, N.S.W. 2033, Australia
John F. Price
Affiliation:
School of MathematicsUniversity of New South WalesKensington, N.S.W. 2033, Australia
Alladi Sitaram
Affiliation:
Stat-Math UnitIndian Statistical InstituteBangalore, 560059, India
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Abstract

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Recently M. Benedicks showed that if a function f ∈ L2(Rd) and its Fourier transform both have supports of finite measure, then f = 0 almot everywhere. In this paper we give a version of this result for all noncompact semisimple connected Lie groups with finite centres.

MSC classification

Secondary: 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. 22E30: Analysis on real and complex Lie groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 45 , Issue 1 , August 1988 , pp. 127 - 132
Copyright
Copyright © Australian Mathematical Society 1988

References

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