Parahyperbolic networks

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In the study of potential theory on an infinite network X or an infinite tree T with terminal vertices, if the Laplacian is not defined at the terminal vertices considering them as boundary points of X, then X always has positive potentials and the constants are harmonic on X. Consequently, the harmonic classification theory of X has to be studied differently from an earlier study which treats T as a Brelot harmonic space.

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