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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