Equilibrium and eigenfunctions estimates in the semi-classical regime

Abstract

We establish eigenfunctions estimates, in the semi-classical regime, for critical energy levels associated to an isolated singularity. For Schrödinger operators, the asymptotic repartition of eigenvectors is the same as in the regular case, excepted in dimension 1 where a concentration at the critical point occurs. This principle extends to pseudo-differential operators and the limit measure is the Liouville measure as long as the singularity remains integrable.

13 pages, 1 figure, perhaps to be revised

References in corpus (4)

• L^p norms of eigenfunctions in the completely integrable case
• A semi-classical trace formula at a totally degenerate critical level
• Semi-classical spectral estimates for Schrödinger operators at a critical level. Case of a degenerate maximum of the potential
• Spectral estimates for degenerate critical levels

Cited by in corpus (1)

• Higher dimensional non standard eigenvalue asymptotics