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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
Published electronically: 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.

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Additional Information

Ivana Alexandrova
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3

Keywords: Semi-classical Schr\"{o}dinger operators, spectral function, Fourier integral operators.
Received by editor(s): March 1, 2005
Published electronically: March 20, 2006
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2006 American Mathematical Society