Semiclassical measures for the Schrödinger equation on the torus

Details Semiclassical measures for the Schrödinger equation on the torus Semiclassical measures for the Schrödinger equation on the torus

2010-04-29

arxiv.org/abs/1005.0296v2

Mathematics

Functional Analysis

We extended Theorem 1 to the case with potential. We added Theorem 4 and modified the organisation of the paper

Scientific paper

In this article, the structure of semiclassical measures for solutions to the linear Schr\"{o}dinger equation on the torus is analysed. We show that the disintegration of such a measure on every invariant lagrangian torus is absolutely continuous with respect to the Lebesgue measure. We obtain an expression of the Radon-Nikodym derivative in terms of the sequence of initial data and show that it satisfies an explicit propagation law. As a consequence, we also prove an observability inequality, saying that the $L^2$-norm of a solution on any open subset of the torus controls the full $L^2$-norm.

Affiliated with

Also associated with

No associations

Rating

Semiclassical measures for the Schrödinger equation on the torus does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Semiclassical measures for the Schrödinger equation on the torus, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Semiclassical measures for the Schrödinger equation on the torus will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-283763