Transformations of linear Hamiltonian difference systems and some of their applications (Q1898945)

The author studies the linear Hamiltonian difference system (LHS) \(\Delta y_n=A_n y_{n+1}+B_n z_n\), \(\Delta z_n=C_n y_{n+1}+A^T_n z_n\), where \(y_n\), \(z_n\) are \(d\)- dimensional \((d\in\mathbb{N})\) sequences, \(A_n\), \(B_n\), \(C_n\) are sequences of real-valued \(d\times d\) matrices, \(A^T_n\) stands for the transpose of the matrix \(A_n\), \(\Delta\) is the usual forward difference operator, \(n\in[M-1,\infty)\), \(M\in\mathbb{N}\). Certain transformations are deduced which transform the above LHS into another LHS.