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Results tagged with micro-local-analysis
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user 144495
4
votes
Weyl law for (non-semiclassical) Schrodinger operator
We are talking about a non-compact Riemannian manifold, right? Then Weyl's law may be incorrect, at least out of the box. Let us consider $H = -\Delta$ (so $V(x)=0$) in the domain $X \subset \mathbb{R …
- 421
4
votes
Intuition behind the Duistermaat-Guillemin version of Weyl's law
Small error: $N(\lambda)$ is a number of eigenvalues $< \lambda^m$ (where $m$ is an order of operator, obviously $m=2$ here). It is not a geometry but a Hamiltonian dynamics (which becomes a Riemannia …
- 421