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Semi-Classical Behavior of the Spectral Function
Ivana Alexandrova
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 Fourie…
Structure of the Short Range Amplitude for General Scattering Relations
Ivana Alexandrova
We consider scattering by short range perturbations of the semi-classical Laplacian. We prove that when a polynomial bound on the resolvent holds, the scattering amplitude is a sem…
Structure of the Semi-Classical Amplitude for General Scattering Relations
Ivana Alexandrova
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 of the…
Semi-Classical Wavefront Set and Fourier Integral Operators
Ivana Alexandrova
We define and prove some properties of the semi-classical wavefront set. We also define and study semi-classical Fourier integral operators, of which we give a complete characteriz…