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Communications in Partial Differential Equations, 30: 15051535, 2005 Copyright Taylor & Francis, Inc.
 

Summary: Communications in Partial Differential Equations, 30: 15051535, 2005
Copyright Taylor & Francis, Inc.
ISSN 0360-5302 print/1532-4133 online
DOI: 10.1080/03605300500299588
Structure of the Semi-Classical Amplitude
for General Scattering Relations
IVANA ALEXANDROVA
Department of Mathematics, University of Toronto, Toronto,
Ontario, Canada
We consider scattering by general compactly supported semi-classical perturbations
of the Euclidean Laplace-Beltrami operator. We show that if the suitably cut-off
resolvent quantizes a Lagrangian relation on the product cotangent bundle, the
scattering amplitude quantizes the natural scattering relation. When we work
microlocally near a non-trapped ray, our result implies that the scattering amplitude
defines a semiclassical Fourier integral operator associated to the scattering relation
in a neighborhood of that ray. Compared to previous work, we allow this relation
to have more general geometric structure.
Keywords Scattering amplitude; Scattering relation; Semi-classical analysis.
Mathematics Subject Classification Primary 35P25; Secondary 35S99.
1. Introduction and Statement of Results

  

Source: Alexandrova, Ivana - Department of Mathematics and Statistics, State University of New York at Albany
Alexandrova, Ivana - Department of Mathematics, East Carolina University

 

Collections: Mathematics