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).
pp. 659-673.
Text
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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 |
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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: | 19 Jan 2023 00:03 |
DOI: | 10.1134/S0001434619110014 |
Related URLs: | |
URI: | https://livrepository.liverpool.ac.uk/id/eprint/3074838 |