English

Uncertainty principles for orthonormal bases

Classical Analysis and ODEs 2007-05-23 v1

Abstract

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as a statement about the time-frequency localization of elements of an orthonormal basis, which improves previous unpublished results of H. Shapiro.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.

Keywords

Cite

@article{arxiv.math/0606396,
  title  = {Uncertainty principles for orthonormal bases},
  author = {Philippe Jaming},
  journal= {arXiv preprint arXiv:math/0606396},
  year   = {2007}
}