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Spectral theory of second-order vector difference equations. (English) Zbl 0934.39002
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.

39A10Additive difference equations
39A12Discrete version of topics in analysis
Full Text: DOI
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