Structure of the Semi-Classical Amplitude for General Scattering Relations |
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Authors: | Ivana Alexandrova |
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Institution: | 1. Department of Mathematics , University of Toronto , Toronto, Ontario, Canada alexandr@math.toronto.edu |
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Abstract: | ABSTRACT 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. In the case when the resolvent is tempered, which is true at non-trapping energies or at trapping energies under some non-resonance assumptions, and 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. |
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Keywords: | Scattering amplitude Scattering relation Semi-classical analysis |
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