A characterization of the locally finite networks admitting non-constant harmonic functions of finite energy

Johannes Carmesin

doi:10.1007/s11118-011-9254-9

A characterization of the locally finite networks admitting non-constant harmonic functions of finite energy

Johannes Carmesin

Mathematics

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5 Citations (Scopus)

Abstract

We characterize the locally finite networks admitting non-constant harmonic functions of finite energy. Our characterization unifies the necessary existence criteria of Thomassen and of Lyons and Peres with the sufficient criterion of Soardi. We also extend a necessary existence criterion for non-elusive non-constant harmonic functions of finite energy due to Georgakopoulos.

Original language	English
Pages (from-to)	229-245
Journal	Potential Analysis
Volume	37
Issue number	3
Early online date	26 Aug 2011
DOIs	https://doi.org/10.1007/s11118-011-9254-9
Publication status	Published - Oct 2012

Keywords

math.CO
31C20, 05C63, 05C81, 05C22
discrete potential theory
linear analysis on graphs
discrete harmonic functions
infinite graphs

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abstract = "We characterize the locally finite networks admitting non-constant harmonic functions of finite energy. Our characterization unifies the necessary existence criteria of Thomassen and of Lyons and Peres with the sufficient criterion of Soardi. We also extend a necessary existence criterion for non-elusive non-constant harmonic functions of finite energy due to Georgakopoulos. ",

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N2 - We characterize the locally finite networks admitting non-constant harmonic functions of finite energy. Our characterization unifies the necessary existence criteria of Thomassen and of Lyons and Peres with the sufficient criterion of Soardi. We also extend a necessary existence criterion for non-elusive non-constant harmonic functions of finite energy due to Georgakopoulos.

AB - We characterize the locally finite networks admitting non-constant harmonic functions of finite energy. Our characterization unifies the necessary existence criteria of Thomassen and of Lyons and Peres with the sufficient criterion of Soardi. We also extend a necessary existence criterion for non-elusive non-constant harmonic functions of finite energy due to Georgakopoulos.

KW - math.CO

KW - 31C20, 05C63, 05C81, 05C22

KW - discrete potential theory

KW - linear analysis on graphs

KW - discrete harmonic functions

KW - infinite graphs

U2 - 10.1007/s11118-011-9254-9

DO - 10.1007/s11118-011-9254-9

M3 - Article

SN - 0926-2601

VL - 37

SP - 229

EP - 245

JO - Potential Analysis

JF - Potential Analysis

IS - 3

ER -

A characterization of the locally finite networks admitting non-constant harmonic functions of finite energy

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Keywords

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