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Benedicks' theorem for the Heisenberg group

Author(s): E. K. Narayanan; P. K. Ratnakumar
Journal: Proc. Amer. Math. Soc. 138 (2010), 2135-2140.
MSC (2010): Primary 42B10; Secondary 22E30, 43A05
Posted: February 4, 2010
MathSciNet review: 2596052
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Abstract | References | Similar articles | Additional information

Abstract: If an integrable function 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 $f \equiv 0.$

References:

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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: 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
Posted: 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
Copyright of article: Copyright 2010, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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