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Journal of the London Mathematical Society 2005 72(3):717-730; doi:10.1112/S0024610705006903
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© The London Mathematical Society

Uncertainty Principles for the Ambiguity Function

Bruno Demange

Université d'Orléans UMR 6628-MAPMO, BP 6759, 45067 Orléans Cedex 2, France bruno.demange{at}univ-orleans.fr

Received 19 April 2004. Revision received 17 February 2005.

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.


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