Semiclassical Defect Measures and Observability Estimate for Schr\"odinger Operators with Homogeneous Potentials of Order Zero
Analysis of PDEs
2025-01-24 v6 Mathematical Physics
math.MP
Spectral Theory
Abstract
We study the asymptotic behavior as |x| \to \infty of Schr\"odinger operators with homogeneous potentials. For this purpose, we use methods from semiclassical analysis and investigate semiclassical defect mesures. We prove their localization in direction which we apply in order to obtain a necessary condition of observability.
Keywords
Cite
@article{arxiv.1811.10428,
title = {Semiclassical Defect Measures and Observability Estimate for Schr\"odinger Operators with Homogeneous Potentials of Order Zero},
author = {Keita Mikami},
journal= {arXiv preprint arXiv:1811.10428},
year = {2025}
}
Comments
24 pages. We improved the statement of the main theorem. We also fixed some mistakes