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Constructing discrete harmonic functions in wedges

Published 2 Nov 2020 in math.SP, math.FA, and math.PR | (2012.08947v2)

Abstract: We propose a systematic construction of signed harmonic functions for discrete Laplacian operators with Dirichlet conditions in the quarter plane. In particular, we prove that the set of harmonic functions is an algebra generated by a single element, which conjecturally corresponds to the unique positive harmonic function.

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