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Recovering the Hamiltonian from spectral data


Authors: C. Hériveaux and T. Paul
Journal: Trans. Amer. Math. Soc. 368 (2016), 7239-7279
MSC (2010): Primary 35-XX, 37-XX, 41-XX, 58-XX, 81-XX
DOI: https://doi.org/10.1090/tran/6566
Published electronically: January 27, 2016
MathSciNet review: 3471090
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Abstract: We show that the contributions to the Gutzwiller formula with observables associated to the iterates of a given elliptic non-degenerate periodic trajectory $ \gamma $ and to certain families of observables localized near $ \gamma $ determine the quantum Hamiltonian in a formal neighborhood of the trajectory $ \gamma $, that is, the full Taylor expansion of its total symbol near $ \gamma $. We also treat the ``bottom of a well'' case both for general and Schrödinger operators, and give some analog classical results.


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Additional Information

C. Hériveaux
Affiliation: CMLS École polytechnique, 91 128 Palaiseau cedex, France
Email: cyrille.heriveaux@math.polytechnique.fr

T. Paul
Affiliation: CNRS and CMLS École polytechnique, 91 128 Palaiseau cedex, France
Email: thierry.paul@polytechnique.edu

DOI: https://doi.org/10.1090/tran/6566
Received by editor(s): November 14, 2013
Received by editor(s) in revised form: September 15, 2014
Published electronically: January 27, 2016
Article copyright: © Copyright 2016 American Mathematical Society