Attractive Coulomb-like Schrödinger operators at low energy: resolvent bounds

The HADES seminar on Tuesday, January 25, will be given by Ethan Sussman at 3:30 pm on Zoom.

Speaker: Ethan Sussman

Abstract: Using techniques recently developed by Vasy to study the limiting absorption principle on asymptotically Euclidean manifolds, we study the effect of an attractive Coulomb-like potential on the resolvent output at low energy. In contrast with the situation for Schrödinger operators with short-range potentials — as analyzed in detail by Guillarmou, Hassell, and Vasy — the spectral family of an attractive Coulomb-like Schrödinger operator fails to degenerate to the same degree as the Laplacian at zero energy. We will see how to use this observation to analyze the output of the limiting resolvent uniformly down to E=0.

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