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Mat. Zametki, 2019, Volume 106, Issue 5, paper published in the English version journal (Mi mz12654)  

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.

Funding Agency Grant Number
Austrian Science Fund W1230
Engineering and Physical Sciences Research Council EP/N014499/1
This first author was supported by the Austrian Science Fund (FWF): W1230, Doctoral Program “Discrete Mathematics.” The second author was partially supported by EPSRC grant EP/N014499/1 (LCMH).



English version:
Mathematical Notes, 2019, 106:5, 659–673

Bibliographic databases:

Received: 08.04.2019
Revised: 02.09.2019
Language:

Citation: T. Boiko, O. Karpenkov, “Martin Integral Representation for Nonharmonic Functions and Discrete Co-Pizzetti Series”, Math. Notes, 106:5 (2019), 659–673

Citation in format AMSBIB
\Bibitem{BoiKar19}
\by T.~Boiko, O.~Karpenkov
\paper Martin Integral Representation for Nonharmonic Functions
and Discrete Co-Pizzetti Series
\jour Math. Notes
\yr 2019
\vol 106
\issue 5
\pages 659--673
\mathnet{http://mi.mathnet.ru/mz12654}
\crossref{https://doi.org/10.1134/S0001434619110014}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000504614300001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85077049242}


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