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Journal Articles Transactions of the American Mathematical Society Year : 2022

Constructing discrete harmonic functions in wedges

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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Dates and versions

hal-02987609 , version 1 (04-11-2020)
hal-02987609 , version 2 (18-01-2023)

Identifiers

Cite

Viet Hung Hoang, Kilian Raschel, Pierre Tarrago. Constructing discrete harmonic functions in wedges. Transactions of the American Mathematical Society, 2022, 375 (7), pp.4741-4782. ⟨10.1090/tran/8615⟩. ⟨hal-02987609v2⟩
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