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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Benedicks' theorem for the Heisenberg group


Authors: E. K. Narayanan and P. K. Ratnakumar
Journal: Proc. Amer. Math. Soc. 138 (2010), 2135-2140
MSC (2010): Primary 42B10; Secondary 22E30, 43A05
Published electronically: February 4, 2010
MathSciNet review: 2596052
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Abstract: If an integrable function $ f$ on the Heisenberg group is supported on the set $ B \times \mathbb{R}$ where $ B \subset \mathbb{C}^n$ is compact and the group Fourier transform $ \hat{f}(\lambda)$ is a finite rank operator for all $ \lambda \in \mathbb{R} \setminus \{0\},$ then $ f \equiv 0.$


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Additional Information

E. K. Narayanan
Affiliation: Department of Mathematics, Indian Institute of Science, Bangalore 12, India
Email: naru@math.iisc.ernet.in

P. K. Ratnakumar
Affiliation: Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211 019, India
Email: ratnapk@hri.res.in

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10272-X
PII: S 0002-9939(10)10272-X
Keywords: Benedicks' theorem, Weyl transform, uncertainty principles.
Received by editor(s): April 15, 2009
Received by editor(s) in revised form: October 28, 2009
Published electronically: February 4, 2010
Additional Notes: The first author was supported in part by a grant from UGC via DSA-SAP
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.