Uncertainty principles for orthonormal bases
Séminaire Équations aux dérivées partielles (Polytechnique) (2005-2006), Talk 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as a statement about the time-frequency localization of elements of an orthonormal basis, which improves previous unpublished results of H. Shapiro.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
Keywords: Uncertainty principles, orthonormal bases
@article{SEDP_2005-2006____A15_0,
     author = {Jaming, Philippe},
     title = {Uncertainty principles for orthonormal bases},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique)},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2005-2006},
     note = {talk:15},
     mrnumber = {2276080},
     language = {en},
     url = {http://www.numdam.org/item/SEDP_2005-2006____A15_0}
}
Jaming, Philippe. Uncertainty principles for orthonormal bases. Séminaire Équations aux dérivées partielles (Polytechnique) (2005-2006), Talk no. 15, 14 p. http://www.numdam.org/item/SEDP_2005-2006____A15_0/

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