Geodesic
$\Phi$-harmonic functions on graphs
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1-9

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We study certain problems of $\Phi$-harmonic analysis on graphs, where $\Phi$ is a strictly convex $N$-function.We introduce the key definitions and reveal that the ones in question are well-defined and what basic properties of harmonic functions hold. Also we prove discrete analogs of classical theorems for harmonic function in the usual sense: uniqueness theorem, Harnack’s inequality, Harnack’s principle etc.
Keywords: $N$-function, $\Phi$-harmonicity, Harnack's inequality, graph. 
@article{SEMR_2017_14_a54,
     author = {R. Panenko},
     title = {$\Phi$-harmonic functions on graphs},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1--9},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a54/}
}
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R. Panenko. $\Phi$-harmonic functions on graphs. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1-9. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a54/