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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Geometric control in the presence of a black box
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by Nicolas Burq and Maciej Zworski PDF
J. Amer. Math. Soc. 17 (2004), 443-471 Request permission

Abstract:

We apply the “black box scattering” point of view to problems in control theory for the Schrödinger equation and in high energy eigenvalue scarring. We show how resolvent bounds with origins in scattering theory, combined with semi-classical propagation, give quantitative control estimates. We also show how they imply control for time dependent problems.
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Additional Information
  • Nicolas Burq
  • Affiliation: Université Paris Sud, Mathématiques, Bât 425, 91405 Orsay Cedex, France
  • MR Author ID: 315457
  • Email: Nicolas.burq@math.u-psud.fr
  • Maciej Zworski
  • Affiliation: Mathematics Department, University of California, Evans Hall, Berkeley, California 94720
  • MR Author ID: 227055
  • Email: zworski@math.berkeley.edu
  • Received by editor(s): May 14, 2003
  • Published electronically: February 3, 2004
  • © Copyright 2004 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 17 (2004), 443-471
  • MSC (2000): Primary 35B37, 35P20, 81Q20
  • DOI: https://doi.org/10.1090/S0894-0347-04-00452-7
  • MathSciNet review: 2051618