Martin Integral Representation for Nonharmonic Functions and Discrete Co-Pizzetti Series



Boiko, T and Karpenkov, O ORCID: 0000-0002-3358-6998
(2019) Martin Integral Representation for Nonharmonic Functions and Discrete Co-Pizzetti Series. MATHEMATICAL NOTES, 106 (5-6). 659 - 673.

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Abstract

In this paper, we study the Martin integral representation for nonharmonic functions in discrete settings of infinite homogeneous trees. Recall that the Martin integral representation for trees is analogs to the mean-value property in Euclidean spaces. In the Euclidean case, the mean-value property for nonharmonic functions is provided by the Pizzetti (and co-Pizzetti) series. We extend the co-Pizzetti series to the discrete case. This provides us with an explicit expression for the discrete mean-value property for nonharmonic functions in discrete settings of infinite homogeneous trees.

Item Type: Article
Uncontrolled Keywords: mean-value property, Laplacian, discrete Laplacian, homogeneous trees, Pizzetti series, co-Pizzetti series
Depositing User: Symplectic Admin
Date Deposited: 27 Feb 2020 16:20
Last Modified: 16 Apr 2021 11:43
DOI: 10.1134/S0001434619110014
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3074838