Equilibrium and eigenfunctions estimates in the semi-classical regime
偏微分方程分析
2015-06-26 v1 数学物理
math.MP
摘要
We establish eigenfunctions estimates, in the semi-classical regime, for critical energy levels associated to an isolated singularity. For Schr\"odinger 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.
引用
@article{arxiv.math/0605637,
title = {Equilibrium and eigenfunctions estimates in the semi-classical regime},
author = {Brice Camus},
journal= {arXiv preprint arXiv:math/0605637},
year = {2015}
}
备注
13 pages, 1 figure, perhaps to be revised