Sharp spectral estimates in domains of infinite volume

Abstract

We consider the Dirichlet Laplace operator on open, quasi-bounded domains of infinite volume. For such domains semiclassical spectral estimates based on the phase-space volume - and therefore on the volume of the domain - must fail. Here we present a method how one can nevertheless prove uniform bounds on eigenvalues and eigenvalue means which are sharp in the semiclassical limit. We give examples in horn-shaped regions and so-called spiny urchins. Some results are extended to Schrödinger operators defined on quasi-bounded domains with Dirichlet boundary conditions.

21 pages, 2 figures

References in corpus (3)

• Two dimensional Berezin-Li-Yau inequalities with a correction term
• Weighted Supermembrane Toy Model
• Universal Bounds for Traces of the Dirichlet Laplace Operator

Cited by in corpus (5)

• Spectral estimates for a class of Schrödinger operators with infinite phase space and potential unbounded from below
• Spectral analysis of a class of Schroedinger operators exhibiting a parameter-dependent spectral transition
• Semiclassical bounds in magnetic bottles
• Improved Berezin-Li-Yau inequalities with magnetic field
• Spectral estimates for Dirichlet Laplacians and Schroedinger operators on geometrically nontrivial cusps