Spectral analysis of one class of matrix differential operators (Q1128372)

This note deals with scattering theory and spectral analysis of a class of matrix operators of the form \[ H=\left( \begin{matrix} (-\Delta)^\ell +q\\ \sum_{| \alpha |< \ell^{(-1)}} \end{matrix} | \alpha |_{\overline v_\alpha D^\alpha} \begin{matrix} \sum_{| \alpha |< \ell} D^\alpha v_\alpha \\ h\end{matrix} \right), \quad H_0= \left(\begin{matrix} (-\Delta)^\ell & 0\\ 0 & h\end{matrix} \right) \] where \(\ell\) is a positive integer, \(v_\alpha\) are bounded functions of class \(C^{| \alpha |}\), \(\alpha \in\mathbb{Z}^n_+\) is a multi-index, \(q\) is a real-valued bounded function and \(h\) is a real-valued continuous function. This class of operators contains, for \(\ell=1\), operators which are associated with the Schrödinger equation with potential depending rationally on the spectral parameter.