Fabricio Macià, Gabriel Riviere
Published 2017-02-07Version 1
In this note, we describe our recent results on semiclassical measures for the Schr{\"o}dinger evolution on Zoll manifolds. We focus on the particular case of eigenmodes of the Schr{\"o}dinger operator on the sphere endowed with its canonical metric. We also recall the relation of this problem with the observability question from control theory. In particular, we exhibit examples of open sets and potentials on the 2-sphere for which observability fails for the evolution problem while it holds for the stationary one. Finally, we give some new results in the case where the Radon transform of the potential identically vanishes.
A remark on the Schrödinger equation on Zoll manifolds
Wigner measures and observability for the Schrödinger equation on the disk
Some remarks on the Schrödinger equation with a potential in $L^{r}_{t}L^{s}_{x}$
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