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Semi-classical behavior of the spectral function
Author:
Ivana Alexandrova
Journal:
Proc. Amer. Math. Soc. 134 (2006), 2295-2302
MSC (2000):
Primary 35P05, 35S99
Posted:
March 20, 2006
MathSciNet review:
2213702
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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
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Alexandrova, Ivana. Semi-Classical Wavefront Set and Fourier Integral Operators. To appear in Canadian Journal of Mathematics.
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Alexandrova, Ivana. Structure of the Semi-Classical Amplitude for General Scattering Relations. Communications in Partial Differential Equations. 2005, 30 (10-12), 1505-1535. MR 2182302
- 3.
Alexandrova, Ivana. Structure of the Short Range Amplitude for General Scattering Relations. Preprint mathAP/0411599 on arxiv.org.
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Arnold, Vladimir. Mathematical Methods of Classical Mechanics. Springer-Verlag. New York, 1980. MR 0690288 (57:14033b)
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Michel, Laurent. Semi-classical Behavior of the Scattering Amplitude for Trapping Perturbations at Fixed Energy. Canadian Journal of Mathematics. 2004, 56, (4), 794-824. MR 2074047 (2005e:35176)
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Robert, Didier and Tamura, Hideo. Asymptotic Behavior of Scattering Amplitudes in Semi-Classical and Low Energy Limits. Annales de l'Institut Fourier. 1989, 39, (1), 155-192. MR 1011982 (91c:35116)
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Vainberg, Boris. Asymptotic Methods in Equations of Mathematical Physics. Gordon and Breach Science Publishers. New York. 1989. MR 1054376 (91h:35081)
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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
DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08463-2
PII:
S 0002-9939(06)08463-2
Keywords:
Semi-classical Schr\"{o}dinger operators,
spectral function,
Fourier integral operators.
Received by editor(s):
March 1, 2005
Posted:
March 20, 2006
Communicated by:
David S. Tartakoff
Article copyright:
© Copyright 2006 American Mathematical Society
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