In this paper an analogous difference operator is studied for an arbitrary graph. It is shown that many properties of the Laplacian in the continuous setting (e.g. the maximum principle, the Harnack ...

The study of differential-difference equations and boundary value problems occupies an essential niche in applied mathematics, linking the theory of differential operators with discrete ...

The maximal dissipative operators with general boundary conditions are investigated. For the dissipative operator, a self-adjoint dilation and is its incoming and outgoing spectral representations are ...