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A description of harmonic functions via properties of the group representation of the Cayley tree. (English) Zbl 1187.43005
Math. Notes 79, No. 3, 399-407 (2006); translation from Mat. Zametki 79, No. 3, 434-443 (2006).
Summary: We introduce a natural generalization of the notion of harmonic functions on a Cayley tree and use some properties of the group representation of the Cayley tree to describe the set of harmonic functions periodic with respect to normal subgroups of finite index.

MSC:
43A65 Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis)
31C05 Harmonic, subharmonic, superharmonic functions on other spaces
20E08 Groups acting on trees
05C05 Trees
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