Hardy's theorem and rotations

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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