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as a statement about the time-frequency localization of elements of an orthonormal basis, which improves previous unpublished results of H. Shapiro.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.
Jaming, Philippe 1
@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) dit aussi "S\'eminaire Goulaouic-Schwartz"},
note = {talk:15},
pages = {1--14},
publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2005-2006},
mrnumber = {2276080},
language = {en},
url = {https://geodesic-test.mathdoc.fr/item/SEDP_2005-2006____A15_0/}
}
TY - JOUR AU - Jaming, Philippe TI - Uncertainty principles for orthonormal bases JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:15 PY - 2005-2006 SP - 1 EP - 14 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - https://geodesic-test.mathdoc.fr/item/SEDP_2005-2006____A15_0/ LA - en ID - SEDP_2005-2006____A15_0 ER -
%0 Journal Article %A Jaming, Philippe %T Uncertainty principles for orthonormal bases %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:15 %D 2005-2006 %P 1-14 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U https://geodesic-test.mathdoc.fr/item/SEDP_2005-2006____A15_0/ %G en %F SEDP_2005-2006____A15_0
Jaming, Philippe. Uncertainty principles for orthonormal bases. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2005-2006), Exposé no. 15, 14 p. https://geodesic-test.mathdoc.fr/item/SEDP_2005-2006____A15_0/