A description of harmonic functions via properties of the group representation of the Cayley tree.

DOI10.1007/S11006-006-0044-4zbMath1187.43005OpenAlexW2039585096MaRDI QIDQ881013

Utkir A. Rozikov, É. P. Normatov

Publication date: 21 May 2007

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11006-006-0044-4

zbMATH Keywords

harmonic functiongroup representationCayley treefinite-index normal subgroupfree product of cyclic groups

Mathematics Subject Classification ID

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

Related Items (10)

Description of \(p\)-harmonic functions on the Cayley tree ⋮ On weakly periodic Gibbs measures for the Potts model with external field on the Cayley tree ⋮ Weakly periodic Gibbs measures of the Ising model with an external field on the Cayley tree ⋮ Description of weakly periodic Gibbs measures for the Ising model on a Cayley tree ⋮ GIBBS MEASURES ON CAYLEY TREES: RESULTS AND OPEN PROBLEMS ⋮ Description of periodic \(p\)-harmonic functions on Cayley tree ⋮ On normal subgroups of the group representation of the Cayley tree ⋮ Entropy Bifurcation of Neural Networks on Cayley Trees ⋮ Invariance property on group representations of the Cayley tree and its applications ⋮ Gibbs measures of Potts model on Cayley trees: A survey and applications

Cites Work

• Description of periodic extreme Gibbs measures of some lattice models on the Cayley tree
• Partition structures of the group representation of the Cayley tree into cosets by finite-index normal subgroups and their applications to the description of periodic Gibbs distributions
• Construction of an uncountable number of limiting Gibbs measures in the inhomogeneous Ising model
• Random walks in random environments of metric groups
• On disordered phase in the ferromagnetic Potts model on the Bethe lattice
• Representability of trees and some of their applications
• Map of fixed points and Lyapunov functions for one class of discrete dynamical systems
• Group representation of the Cayley forest and some of its applications
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