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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Recovering the Hamiltonian from spectral data
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by C. Hériveaux and T. Paul PDF
Trans. Amer. Math. Soc. 368 (2016), 7239-7279 Request permission

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
  • Received by editor(s): November 14, 2013
  • Received by editor(s) in revised form: September 15, 2014
  • Published electronically: January 27, 2016
  • © Copyright 2016 American Mathematical Society
  • 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
  • MathSciNet review: 3471090