Discrete Laplace Operator - Discrete Green's Function

Discrete Green's Function

The Green's function of the discrete Schrödinger operator is given in the resolvent formalism by

where is understood to be the Kronecker delta function on the graph: ; that is, it equals 1 if v=w and 0 otherwise.

For fixed and a complex number, the Green's function considered to be a function of v is the unique solution to

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