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HARDY’S THEOREM AND ROTATIONS

Hogan, Jeffrey A. and Lakey, Joseph D. (2006) HARDY’S THEOREM AND ROTATIONS. Proceedings of the American Mathematical Society, 134 (5). pp. 1459-1466. ISSN 0002-9939

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    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 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 $f$ and its Fourier transform $\hat{f}$ along some pair of lines in the complex plane is shown to imply that $f$ is a complex Gaussian.

    Item Type: Article
    Uncontrolled Keywords: Hardy's theorem, uncertainty principle
    Subjects: 30-xx Functions of a complex variable
    42-xx Fourier analysis > 42Axx Fourier analysis in one variable
    Faculty: UNSPECIFIED
    Depositing User: Mr Christopher Maitland
    Date Deposited: 29 Jun 2011 16:48
    Last Modified: 29 Jun 2011 16:48
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/877

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