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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Semi-classical behavior of the spectral function
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by Ivana Alexandrova PDF
Proc. Amer. Math. Soc. 134 (2006), 2295-2302 Request permission

Abstract:

We study the semi-classical behavior of the spectral function of the Schrödinger operator with short range potential. We prove that the spectral function is a semi-classical Fourier integral operator quantizing the forward and backward Hamiltonian flow relations of the system. Under a certain geometric condition we explicitly compute the phase in an oscillatory integral representation of the spectral function.
References
  • Alexandrova, Ivana. Semi-Classical Wavefront Set and Fourier Integral Operators. To appear in Canadian Journal of Mathematics.
  • Ivana Alexandrova, Structure of the semi-classical amplitude for general scattering relations, Comm. Partial Differential Equations 30 (2005), no. 10-12, 1505–1535. MR 2182302, DOI 10.1080/03605300500299588
  • Alexandrova, Ivana. Structure of the Short Range Amplitude for General Scattering Relations. Preprint mathAP/0411599 on arxiv.org.
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Additional Information
  • Ivana Alexandrova
  • Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
  • Email: alexandr@math.toronto.edu
  • Received by editor(s): March 1, 2005
  • Published electronically: March 20, 2006
  • Communicated by: David S. Tartakoff
  • © Copyright 2006 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 2295-2302
  • MSC (2000): Primary 35P05, 35S99
  • DOI: https://doi.org/10.1090/S0002-9939-06-08463-2
  • MathSciNet review: 2213702