Uncertainty principles for orthonormal bases
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as a statement about the time-frequency localization of elements of an orthonormal basis, which improves previous unpublished results of H. Shapiro.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
Jaming, Philippe 1

1 Université d’Orléans Faculté des Sciences MAPMO - Fédération Denis Poisson BP 6759 F 45067 Orléans Cedex 2 France
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Jaming, Philippe. Uncertainty principles for orthonormal bases. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2005-2006), Exposé no. 15, 14 p. http://archive.numdam.org/item/SEDP_2005-2006____A15_0/

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