- 98-696 Yafaev D.
- A model of perturbation theory
(73K, PostScript)
Nov 2, 98
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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
${\bf H}$.
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