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UNCERTAINTY PRINCIPLES FOR THE AMBIGUITY FUNCTION

Published online by Cambridge University Press:  08 December 2005

BRUNO DEMANGE
BRUNO DEMANGE
Affiliation:
Université d'Orléans, UMR 6628-MAPMO, BP 6759, 45067 Orléans Cedex 2, Francebruno.demange@univ-orleans.fr
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Abstract

We extend uncertainty principles which are valid for the Fourier transform to the setting of the ambiguity function. A general result is established for annihilating sets: strongly/weakly annihilating sets for the Fourier transform yield such sets for the ambiguity function, extending a result known for sets of finite measure. We apply this to sublevel sets of nondegenerate quadratic forms. Our main result is a sharp version of Beurling's uncertainty principle for the ambiguity function.

Keywords

42B1033C4594A12
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 72 , Issue 3 , December 2005 , pp. 717 - 730
Copyright
The London Mathematical Society 2005

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