Hardy's theorem and rotations

Authors:
J. A. Hogan and J. D. Lakey

Journal:
Proc. Amer. Math. Soc. **134** (2006), 1459-1466

MSC (2000):
Primary 42A38; Secondary 30D15

DOI:
https://doi.org/10.1090/S0002-9939-05-08098-6

Published electronically:
October 18, 2005

MathSciNet review:
2199193

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove an extension of Hardy's classical characterization of real Gaussians of the form , , to the case of complex Gaussians in which is a complex number with positive real part. Such functions represent rotations in the complex plane of real Gaussians. A condition on the rate of decay of analytic extensions of a function and its Fourier transform along some pair of lines in the complex plane is shown to imply that is a complex Gaussian.

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Additional Information

**J. A. Hogan**

Affiliation:
Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701

Email:
jeffh@uark.edu

**J. D. Lakey**

Affiliation:
Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003–8001

Email:
jlakey@nmsu.edu

DOI:
https://doi.org/10.1090/S0002-9939-05-08098-6

Keywords:
Hardy's theorem,
uncertainty principle

Received by editor(s):
September 24, 2004

Received by editor(s) in revised form:
December 20, 2004

Published electronically:
October 18, 2005

Additional Notes:
This research was supported by a Macquarie University MURG grant

Communicated by:
Juha M. Heinonen

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.