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A qualitative uncertainty principle for semisimple Lie groups

Part of: Abstract harmonic analysis Lie groups

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

[1]Anker, J.-Ph., ‘Applications de la p-induction en analyse harmonique’, Comment. Math. Helv. 58 (1983), 622–645.CrossRefGoogle Scholar
[2]Benedicks, M., ‘On Fourier transforms of functions supported on sets of finite Lebesgue measure’, J. Math. Anal. Appl. 10 (1985), 180–183.CrossRefGoogle Scholar
[3]Cowling, M., ‘The Kunze-Stein phenomenon’, Ann. of Math. 107 (1978), 209–234.CrossRefGoogle Scholar
[4]Cowling, M. G. and Price, J. F., ‘Bandwith versus time concentration: the Heisenberg-Pauli-Weyl inequality’, SIAM J. Math. Anal. 15 (1984), 151–165.Google Scholar
[5]Dym, H. and McKean, H. P., Fourier Series and Integrals (Academic Press, 1972).Google Scholar
[6]Harish-Chandra, , ‘Harmonic analysis on real Lie groups III’, Ann. of Math. 104 (1976), 117–201.CrossRefGoogle Scholar
[7]Price, J. F. and Sitaram, A., ‘Functions and their Fourier transforms with supports of finite measure for certain locally compact groups’, J. Funct. Anal. (to appear).Google Scholar
[8]Price, J. F. and Sitaram, A., ‘Local uncertainty inequalities for locally compact groups’, Trans. Amer. Math. Soc. (to appear).Google Scholar
[9]Price, J. F. and Sitaram, A., ‘Local uncertainty inequalities for compact groups’, Proc. Amer. Math. Soc. (to appear).Google Scholar
[10]Vogan, D. A., ‘Representations of semisimple Lie groups I’, Ann. of Math. 109 (1979), 1–60.CrossRefGoogle Scholar
[11]Warner, G., Harmonic Analysis on Semi-Simple Lie Groups, Vol. I (Springer-Verlag, 1972).Google Scholar