Yafaev D.
A model of perturbation theory
(73K, PostScript)

ABSTRACT.  We consider a model of the  perturbation theory  where the Hamiltonian ${\bf H}$ is 
a sum of 
a multiplication operator ${\bf H}_0$  by
$|x|^{2l}$   in the space
$L_2({\Bbb R}^d)$ and of an integral operator ${\bf V}$ with    oscillating kernel.
We find conditions for the coincidence of the essential spectra of the operators ${
\bf H}_0$ and
${\bf H}$ and for the existence and completeness of the wave operators relating ${\
bf H}_0$ and
${\bf H}$.