Spectral analysis for differential systems with a singularity

Abstract

We consider the differential system $y^{\prime }-x^{-1}Ay-q(x)y=\rho By$ with $n\times n$ matrices $A,B,q(x)$, where $A,B$ are constant, $B$ is diagonal, $A$ and $q(x)$ are off-diagonal, $q(\cdot )\in W_1^1[0,\infty )$. Some distinguished fundamental system of solutions is constructed. Also, we discuss the inverse scattering problem and obtain the uniqueness result.