Uncertainty principles for orthonormal bases

Philippe Jaming[1]

  • [1] Université d’Orléans Faculté des Sciences MAPMO - Fédération Denis Poisson BP 6759 F 45067 Orléans Cedex 2 France

Séminaire Équations aux dérivées partielles (2005-2006)

  • Volume: 2005-2006, page 1-14

Abstract

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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as a statement about the time-frequency localization of elements of an orthonormal basis, which improves previous unpublished results of H. Shapiro.Finally, we reformulate some uncertainty principles in terms of properties of the free heat and shrödinger equations.

How to cite

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Jaming, Philippe. "Uncertainty principles for orthonormal bases." Séminaire Équations aux dérivées partielles 2005-2006 (2005-2006): 1-14. <http://eudml.org/doc/11127>.

@article{Jaming2005-2006,
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as a statement about the time-frequency localization of elements of an orthonormal basis, which improves previous unpublished results of H. Shapiro.Finally, we reformulate some uncertainty principles in terms of properties of the free heat and shrödinger equations.},
affiliation = {Université d’Orléans Faculté des Sciences MAPMO - Fédération Denis Poisson BP 6759 F 45067 Orléans Cedex 2 France},
author = {Jaming, Philippe},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {Uncertainty principles; orthonormal bases},
language = {eng},
pages = {1-14},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Uncertainty principles for orthonormal bases},
url = {http://eudml.org/doc/11127},
volume = {2005-2006},
year = {2005-2006},
}

TY - JOUR
AU - Jaming, Philippe
TI - Uncertainty principles for orthonormal bases
JO - Séminaire Équations aux dérivées partielles
PY - 2005-2006
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2005-2006
SP - 1
EP - 14
AB - 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.
LA - eng
KW - Uncertainty principles; orthonormal bases
UR - http://eudml.org/doc/11127
ER -

References

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