A transformation of right-definite S-Hermitian systems to canonical systems (Q2644838)

In this note, the first order system of differential equations (*) \(F_{11}y'+F_{12}y=\lambda (G_{11}y'+G_{12}y)\) on the compact interval \(I=[a,b]\) is considered. It is assumed that the \(n\times n\) matrix functions \(F_{1j}\), \(G_{1j}\), \(j=1,2\), are continuous on I and that \(F_{11}(x)-\lambda G_{11}(x)\) is invertible for all \(x\in I\) and \(\lambda\in R\). It is shown that right-definite S-Hermitian boundary value problems, which are defined in this note, can be reduced to canonical systems with selfadjoint boundary conditions in such a way that the transformed boundary conditions become a special case of those considered by other authors.