An uncertainty principle related to the Poisson summation formula
Gröchenig, K.
Studia Mathematica, Tome 119 (1996), p. 87-104 / Harvested from The Polish Digital Mathematics Library
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We prove a class of uncertainty principles of the form ∥Sgf∥1≤C(∥xaf∥p+∥ωbf̂∥q), where Sgf is the short time Fourier transform of f. We obtain a characterization of the range of parameters a,b,p,q for which such an uncertainty principle holds. Counter-examples are constructed using Gabor expansions and unimodular polynomials. These uncertainty principles relate the decay of f and f̂ to their behaviour in phase space. Two applications are given: (a) If such an inequality holds, then the Poisson summation formula is valid with absolute convergence of both sums. (b) The validity of an uncertainty principle implies sufficient conditions on a symbol σ such that the corresponding pseudodifferential operator is of trace class.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:216344 
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     title = {An uncertainty principle related to the Poisson summation formula},
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     volume = {119},
     year = {1996},
     pages = {87-104},
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Gröchenig, K. An uncertainty principle related to the Poisson summation formula. Studia Mathematica, Tome 119 (1996) pp. 87-104. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv121i1p87bwm/

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