Spectral theory of second-order vector difference equations
The paper deals with the boundary value problem \[ -\nabla (C_n\Delta x_n)+B_nx_n= \lambda\omega_n x_n,\quad n=1,2, \dots,N, \] \[ R{-x_0 \choose x_N}+ S{C_0\Delta x_0\choose C_N\Delta x_N}=0, \] where the matrices \(C_n\) may be singular. After a suitable definition of self-adjointness, corresponding spectral results, the dual orthogonality, Rayleigh's principles, minimax theorems and a comparison theorem for eigenvalues are obtained.
scientific article; zbMATH DE number 1384918