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SUMMARY:Spectral Uncertainty Principles for Laplace-Beltrami and Schrödin
ger Operators
DTSTART:20231012T143000Z
DTEND:20231012T153000Z
DTSTAMP:20240529T124200Z
UID:indico-event-10686@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Iván Moyano (Université Côte-d'Azur & Imperical C
ollege\, London)\n\nIn this talk we review some classical and recent resul
ts relating the uncertainty principles for the Laplacian with the controll
ability and stabilisation of some linear PDEs. The uncertainty principles
for the Fourier transforms state that a square integrable function cannot
be both localised in frequency and space without being zero\, and this can
be further quantified resulting in unique continuation inequalities in th
e phase spaces. Applying these ideas to the spectrum of the Laplacian on a
compact Riemannian manifold\, Lebeau and Robbiano obtained their celebrat
ed result on the exact controllability of the heat equation in arbitrarily
small time. The relevant quantitative uncertainty principles known as spe
ctral inequalities in the literature can be adapted to a number of differe
nt operators\, including the Laplace-Beltami operator associated to $C^1$
metrics or some Schödinger operators with long-range potentials\, as we h
ave shown in recent results in collaboration with Gilles Lebeau (Nice) and
Nicolas Burq (Orsay)\, with a significant relaxation on the localisation
in space. As a consequence\, we obtain a number of corollaries on the deca
y rate of damped waves with rough dampings\, the simultaneous controllabil
ity of heat equations with different boundary conditions and the controlla
bility of the heat equation with rough controls.\n\nhttps://indico.math.cn
rs.fr/event/10686/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/10686/
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