É. P. Normatov, U. A. Rozikov, “A description of harmonic functions via properties of the group representation of the Cayley tree”, Mat. Zametki, 79:3 (2006), 434–443; Math. Notes, 79:3 (2006), 399

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Matematicheskie Zametki, 2006, Volume 79, Issue 3, Pages 434–443
DOI: https://doi.org/10.4213/mzm2712 (Mi mzm2712)

This article is cited in 12 scientific papers (total in 12 papers)

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

É. P. Normatov^a, U. A. Rozikov^b

^a National University of Uzbekistan named after M. Ulugbek
^b Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Full-text PDF (244 kB) Citations (12)

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DOI: https://doi.org/10.4213/mzm2712

Abstract: 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.

Received: 11.11.2004

English version:
Mathematical Notes, 2006, Volume 79, Issue 3, Pages 399–407
DOI: https://doi.org/10.1007/s11006-006-0044-4

Bibliographic databases:

UDC: 512.544.23+517.98+519.21

Language: Russian

Citation: É. P. Normatov, U. A. Rozikov, “A description of harmonic functions via properties of the group representation of the Cayley tree”, Mat. Zametki, 79:3 (2006), 434–443; Math. Notes, 79:3 (2006), 399–407

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm2712

https://doi.org/10.4213/mzm2712

https://www.mathnet.ru/eng/mzm/v79/i3/p434

This publication is cited in the following 12 articles:

F. H. Haydarov, “On normal subgroups of the group representation of the Cayley tree”, Vladikavk. matem. zhurn., 25:4 (2023), 135–142
Farhod Haydarov, Utkir Rozikov, “Invariance Property on Group Representations of the Cayley Tree and Its Applications”, Results Math, 77:6 (2022)
Rozikov U.A., “Gibbs Measures of Potts Model on Cayley Trees: a Survey and Applications”, Rev. Math. Phys., 33:10 (2021), 2130007
M. M. Rakhmatullaev, Zh. D. Dekhkonov, “Suschestvovanie slabo periodicheskikh mer Gibbsa dlya modeli Izinga na dereve Keli poryadka tri”, Vladikavk. matem. zhurn., 23:4 (2021), 77–88
Ban J.-Ch., Chang Ch.-H., Huang N.-Zh., “Entropy Bifurcation of Neural Networks on Cayley Trees”, Int. J. Bifurcation Chaos, 30:1 (2020), 2050015
Rakhmatullaev M.M., “On Weakly Periodic Gibbs Measures for the Potts Model with External Field on the Cayley Tree”, Ukr. Math. J., 68:4 (2016), 598–611
M. M. Rakhmatullaev, “Weakly periodic Gibbs measures of the Ising model with an external field on the Cayley tree”, Theoret. and Math. Phys., 183:3 (2015), 822–828
Tuncer A., Erzan A., “Spectral Renormalization Group For the Gaussian Model and Psi(4) Theory on Nonspatial Networks”, Phys. Rev. E, 92:2 (2015), 022106
Rozikov U.A., “Gibbs Measures on Cayley Trees: Results and Open Problems”, Rev. Math. Phys., 25:1 (2013), 1330001
U. A. Rozikov, F. T. Ishankulov, “Description of $p$-harmonic functions on the Cayley tree”, Theoret. and Math. Phys., 162:2 (2010), 222–229
Rozikov U.A., Ishankulov F.T., “Description of periodic $p$-harmonic functions on Cayley tree”, NoDEA Nonlinear Differential Equations Appl., 17:2 (2010), 153–160
U. A. Rozikov, M. M. Rakhmatullaev, “Description of weakly periodic Gibbs measures for the Ising model on a Cayley tree”, Theoret. and Math. Phys., 156:2 (2008), 1218–1227

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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