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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Official URL: http://www.ams.org/journals/proc/2006-134-05/S0002...

## 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 |
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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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