Ilya Kachkovskiy (KCL)

Stein-Tomas theorem for a torus and an application to the periodic Schrodinger operator

Abstract:
We prove an analogue of Stein-Tomas theorem for a torus except for the endpoint case. The result can be applied to establishing absolute continuity of the spectrum of the four-dimensional periodic Schrodinger operator with delta-like potential concentrated on a hypersurface of nonzero curvature.