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ЖУРНАЛЫ // Математические заметки // Архив

Матем. заметки, 2019, том 106, выпуск 5, страницы 659–673 (Mi mzm12654)

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

Язык публикации: английский


 Англоязычная версия: Mathematical Notes, 2019, 106:5, 659–673

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