Uncertainty principles for orthonormal bases

Philippe Jaming (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

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as a statement about the time-frequency localization of elements of an orthonormal basis, which improves previous unpublished results of H. Shapiro.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 show that Benedicks' result implies that solutions of the Shrödinger equation have some (appearently unnoticed) energy dissipation property.

Mots clés: Uncertainty principles; orthonormal bases

Domaines: Analyse classique [math.CA]

Philippe Jaming. Uncertainty principles for orthonormal bases. Seminaire d'equations aux derivees partielles, 2006, Palayseau, France. expose XV, 21 fevrier 2006. ⟨hal-00080458⟩