Ivana Alexandrova

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We study the scattering amplitude for Schrödinger operators at a critical energy level, which is a unique nondegenerate maximum of the potential. We do not assume that the maximum point is non-resonant and use results by Bony, Fujiié, Ramond and Zerzeri to analyze the contributions of the trapped trajectories. We prove a semiclassical expansion of the(More)
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 semi-classical Fourier integral operator associated to the scattering relation near a non-trapped ray. Compared to previous work, we allow the scattering relation to have more general(More)
The existence of the Laplace-Beltrami operator has allowed mathematicians to carry out Fourier analysis on Riemannian manifolds [2]. We recall that the Laplace-Beltrami operator ∆ on a compact Riemannian manifold has a discrete set of eigenvalues {λj}j=1, which satisfies λj →∞ as j →∞. This is known as the spectrum of the Laplace-Beltrami operator. Inverse(More)
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 semiclassical 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(More)
We consider the problem of quantum resonances in magnetic scattering by two solenoidal fields at large separation in two dimensions. This system has trapped trajectories oscillating between two centers of the fields. We give a sharp lower bound on resonance widths when the distance between the two centers goes to infinity. The bound is described in terms of(More)
We study the microlocal structure of the resolvent of the semiclassical Schrödinger operator with short range potential at an energy which is a unique non-degenerate global maximum of the potential. We prove that it is a semiclassical Fourier integral operator quantizing the incoming and outgoing Lagrangian submanifolds associated to the fixed hyperbolic(More)
We analyze the microlocal structure of the semi-classical scattering amplitude for Schrödinger operators with a strong magnetic and a strong electric fields at non-trapping energies. For this purpose we develop a framework and establish some of the properties of semi-classical-Fourier-integral-operatorvalued pseudodifferential operators and prove that the(More)