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Uncertainty Principles for the Ambiguity Function
Author(s) -
Demange Bruno
Publication year - 2005
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610705006903
Subject(s) - ambiguity , ambiguity function , fourier transform , function (biology) , mathematics , measure (data warehouse) , quadratic equation , uncertainty principle , mathematical analysis , pure mathematics , computer science , physics , data mining , quantum mechanics , geometry , evolutionary biology , waveform , biology , programming language , voltage , quantum
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.