Uncertainty principles for orthonormal bases

Jaming, Philippe

Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2005-2006), Exposé no. 15, 14 p.

In this survey, we present various forms of the uncertainty principle (Hardy, Heisenberg, Benedicks...). We further give a new interpretation of the uncertainty principles as a statement about the time-frequency localization of elements of an orthonormal basis, which improves previous unpublished results of H. Shapiro.

Finally, we reformulate some uncertainty principles in terms of properties of the free heat and shrödinger equations.

Classification : 42B10
Mots clés : Uncertainty principles, orthonormal bases

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