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A Semi-Classical Trace Formula at a Totally Degenerate Critical Level

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Abstract

We study the semi-classical trace formula at a critical energy level for an h-pseudo-differential operator on n whose principal symbol has a totally degenerate critical point for that energy. This problem is studied for a large time behavior and under the hypothesis that the principal symbol of the operator has a local extremum at the critical point.

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Authors and Affiliations

  1. Mathematisches Institut der Ludwig-Maximilians-Universität München, Theresienstraße 39, 80333, Munich, Germany

    Brice Camus

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  1. Brice Camus
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Correspondence to Brice Camus.

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P. Sarnak

This work was supported by the IHP-Network Analysis and Quantum, reference number HPRN-CT-2002-00277. We thank Raymond Brummelhuis for encouragement and for advice concerning this work. We also thank Bernard Helffer for constructive remarks on this work.

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Camus, B. A Semi-Classical Trace Formula at a Totally Degenerate Critical Level. Commun. Math. Phys. 247, 513–526 (2004). https://doi.org/10.1007/s00220-004-1068-9

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  • DOI: https://doi.org/10.1007/s00220-004-1068-9

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