# Generalized Fourier transform for $C^2$ potentials

Kenichi Ito (Graduate School of Mathematical Sciences, University of Tokyo)
Onsdag 29. marts 2023 16:15–17:15 Aud. D3 (1531-215)
Mathematics seminar

We construct the generalized Fourier transforms for the Schr\"odinger operator with a $C^2$ long-range potential. For the construction we regularize the potential following H\"ormander, and solve the associated eikonal equation. Then, using the solution, we derive strong forms of radiation condition bounds for the associated limiting resolvents. These bounds improve formerly known ones, and much simplify the above construction. For proof of these bounds we employ an elementary commutator argument with a second order differential operator as conjugate operator.

Kontakt: Erik Skibsted Revideret: 17.03.2023