An inverse problem for the quadratic pencil of non-self-adjoint matrix operators on the half-line (Q2877845)

The authors consider the pencil of matrix Sturm-Liouville operators on the half-line \(x > 0\) in the form NEWLINE\[NEWLINE \ell_{\rho}(Y) = Y'' + (\rho^2 I + 2 i \rho Q_1(x) + Q_0(0)) Y, NEWLINE\]NEWLINE NEWLINE\[NEWLINE Y'(0) + (i \rho h_1 + h_0) Y(0) = 0. NEWLINE\]NEWLINE The general non-self-adjoint case is investigated. The inverse problem is studied, which consists in recovering the coefficients of the pencil by the Weyl matrix. The authors prove a uniqueness theorem and present a constructive solution of the inverse problem, based on the method of spectral mappings.