The theory of V-Bézoutians and its applications (Q1344077)

A regular matrix boundary value problem that contains the eigenvalue parameter in the boundary conditions is considered. Using the theory of V. Bézoutians, the author shows how this BVP yields a self-adjoint problem in the appropriate Pontryagin space \(\Pi_ \kappa\). Namely, the indefinite scalar product in \(\Pi_ \kappa\) is constructed with the help of V. Bézoutians of matrix polynomials entering the boundary conditions. The following three special cases: a) the Sturm-Liouville problem; b) the generalized periodic problem; c) the crossed boundary problem are studied.