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Semiclassical spectral estimates for Schrödinger operators at a critical energy level. Case of a degenerate minimum of the potential

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
341
Issue
2
Identifiers
DOI: 10.1016/j.jmaa.2007.10.074
Keywords
  • Trace Formula
  • Semi-Classical Analysis
  • Schrödinger Operators

Abstract

Abstract We study the semi-classical trace formula at a critical energy level for a Schrödinger operator on R n . We assume here that the potential has a totally degenerate critical point associated to a local minimum. The main result, which computes the contribution of this equilibrium, is valid for all time in a compact and establishes the existence of a total asymptotic expansion whose top order coefficient depends only on the germ of the potential at the critical point.

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