3 papers
math.AP2025
Geometry of wave damping on the torus
Kiril Datchev, Perry Kleinhenz, Antoine Prouff
Energy decay rates of damped waves on the torus depend on the behavior of the damping near the undamped region and on the geometry of the damped set. In this paper we refine these…
math.AP2024
Egorov's theorem in the Weyl--Hörmander calculus
Antoine Prouff
We prove a general version of Egorov's theorem for evolution propagators in the Euclidean space, in the Weyl--Hörmander framework of metrics on the phase space. Mild assumptions o…
math.AP2024
Smoothing effect and quantum-classical correspondence for the Schr{ö}dinger equation with confining potential
Antoine Prouff
The smoothing effect states that solutions to the Schr{ö}dinger equation in the Euclidean space have, for almost-every time, a local-in-space improved regularity (gain of half a d…