Uncertainty principles for orthonormal bases

Details Uncertainty principles for orthonormal bases Uncertainty principles for orthonormal bases

2006-06-16

arxiv.org/abs/math/0606396v1

Seminaire d'equations aux derivees partielles, France (2006) expose XV, 21 fevrier 2006

Mathematics

Classical Analysis and ODEs

Scientific paper

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as a statement about the time-frequency localization of elements of an orthonormal basis, which improves previous unpublished results of H. Shapiro.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 Shr\"{o}dinger equation have some (appearently unnoticed) energy dissipation property.

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