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VARIANTS OF MIYACHI’S THEOREM FOR NILPOTENT LIE GROUPS

Part of: Lie groups

Published online by Cambridge University Press:  19 January 2010

ALI BAKLOUTI  and
SUNDARAM THANGAVELU
ALI BAKLOUTI
Affiliation:
Department of Mathematics, Faculty of Sciences at Sfax, Route de Soukra, 3038, Sfax, Tunisia (email: Ali.Baklouti@fss.rnu.tn)
SUNDARAM THANGAVELU*
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore 560012, India (email: veluma@math.iisc.ernet.in)
*
✉For correspondence; e-mail: veluma@math.iisc.ernet.in
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Abstract

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We formulate and prove two versions of Miyachi’s theorem for connected, simply connected nilpotent Lie groups. This allows us to prove the sharpness of the constant 1/4 in the theorems of Hardy and of Cowling and Price for any nilpotent Lie group. These theorems are proved using a variant of Miyachi’s theorem for the group Fourier transform.

Keywords

uncertainty principlesPlancherel formulanilpotent Lie group

MSC classification

Secondary: 22E25: Nilpotent and solvable Lie groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 88 , Issue 1 , February 2010 , pp. 1 - 17
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

The first author was supported by D.G.R.S.R.T., Research Unity 00 UR 1501 and the second author by a J.C. Bose Fellowship from DST.

References

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