Non-selfadjoint matrix Sturm-Liouville operators with spectral singularities
Consider the operator \(L\), generated in the space \(L^2(\mathbb R_+,\mathbb R^n)\) by the matrix differential expression \[ l(y)=-y''+Q(x)y,\quad x\in\mathbb R_+ \] and the boundary condition \(y(0)=0\), where \(Q:\mathbb R_+\to\mathbb R^n\) is a non-selfadjoint matrix-valued function. If \(\sup_{x\in\mathbb R_+}[\exp(\varepsilon\sqrt x)\|Q(x)\|]<\infty\), \(\varepsilon>0\), the authors prove that \(L\) has a finite number of eigenvalues and spectral singularities and each of them is of finite multiplicity.
scientific article; zbMATH DE number 5736345
scientific article