Generalized Fourier Transform for Schrodinger Operators with Potentials of Order Zero

摘要

We investigate the Schrodinger operator H=- triangle open+V acting in L~2(R~n), n>=2, for potentials V that satisfy partial deriv~(#alpha#)_xV(x)=O(|x|~(-|#alpha#|)) as |x|-> infinity. By introducing coordinates on R~n closely related to a relevant eikonal equation we obtain an eigenfunction expansion for H at high energies.