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Математические заметки, 2019, том 106, выпуск 5, статья опубликована в англоязычной версии журнала
(Mi mzm12654)
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Статьи, опубликованные в английской версии журнала
Martin Integral Representation for Nonharmonic Functions
and Discrete Co-Pizzetti Series
T. Boiko, O. Karpenkov University of Liverpool, Liverpool, L69 3BX UK
Аннотация:
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.
Ключевые слова:
mean-value property, Laplacian, discrete Laplacian, homogeneous trees, Pizzetti series,
co-Pizzetti series.
Поступило: 08.04.2019 Исправленный вариант: 02.09.2019
Образец цитирования:
T. Boiko, O. Karpenkov, “Martin Integral Representation for Nonharmonic Functions
and Discrete Co-Pizzetti Series”, Math. Notes, 106:5 (2019), 659–673
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/mzm12654
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Страница аннотации: | 102 |
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