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Constructing discrete harmonic functions in wedges
Viet Hung Hoang, Kilian Raschel, Pierre Tarrago · 2020-11-02 · via math.PR updates on arXiv.org

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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