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Matematicheskie Zametki, 2019, Volume 106, Issue 5, paper published in the English version journal
(Mi mzm12654)
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Papers published in the English version of the journal
Martin Integral Representation for Nonharmonic Functions
and Discrete Co-Pizzetti Series
T. Boiko, O. Karpenkov University of Liverpool, Liverpool, L69 3BX UK
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.
Keywords:
mean-value property, Laplacian, discrete Laplacian, homogeneous trees, Pizzetti series,
co-Pizzetti series.
Received: 08.04.2019 Revised: 02.09.2019
Citation:
T. Boiko, O. Karpenkov, “Martin Integral Representation for Nonharmonic Functions
and Discrete Co-Pizzetti Series”, Math. Notes, 106:5 (2019), 659–673
Linking options:
https://www.mathnet.ru/eng/mzm12654
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Abstract page: | 94 |
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