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Equilibrium and eigenfunctions estimates in the semi-classical regime

Brice Camus
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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.

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Brice Camus. 2006-05-24. Equilibrium and eigenfunctions estimates in the semi-classical regime. https://doi.org/10.1063/1.2378619

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