- Title
- Hardy's theorem and rotations
- Creator
- Hogan, J. A.; Lakey, J. D.
- Relation
- Proceedings of the American Mathematical Society Vol. 134, Issue 5, p. 1459 - 1466
- Relation
- http://www.ams.org/journals/proc/2006-134-05/S0002-9939-05-08098-6
- Publisher
- American Mathematical Society
- Resource Type
- journal article
- Date
- 2006
- Description
- We prove an extension of Hardy’s classical characterization of real Gaussians of the form e−παx2, α > 0, to the case of complex Gaussians in which α 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 ƒ and its Fourier transform ƒ̂ along some pair of lines in the complex plane is shown to imply that ƒ is a complex Gaussian.
- Subject
- Hardy’s theorem; uncertainty principle
- Identifier
- http://hdl.handle.net/1959.13/926924
- Identifier
- uon:9987
- Identifier
- ISSN:0002-9939
- Language
- eng
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