Constructing discrete harmonic functions in wedges

Hoang, Viet; Raschel, Kilian; Tarrago, Pierre

doi:10.1090/tran/8615

Constructing discrete harmonic functions in wedges
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by Viet Hung Hoang, Kilian Raschel and Pierre Tarrago PDF

Trans. Amer. Math. Soc. 375 (2022), 4741-4782 Request permission

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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