Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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
Posted: 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 $e^{-\pi\alpha x^2}$ , $\alpha>0$ , to the case of complex Gaussians in which $\alpha$ 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 $\widehat f$ along some pair of lines in the complex plane is shown to imply that is a complex Gaussian.

References

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