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Mat. Zametki, 2006, Volume 79, Issue 3, Pages 434–443 (Mi mz2712)  

This article is cited in 7 scientific papers (total in 7 papers)

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

É. P. Normatova, U. A. Rozikovb

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

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.

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

Full text: PDF file (244 kB)
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English version:
Mathematical Notes, 2006, 79:3, 399–407

Bibliographic databases:

UDC: 512.544.23+517.98+519.21
Received: 11.11.2004

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

    This publication is cited in the following articles:
    1. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. U. A. Rozikov, F. T. Ishankulov, “Description of $p$-harmonic functions on the Cayley tree”, Theoret. and Math. Phys., 162:2 (2010), 222–229  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. 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  crossref  mathscinet  zmath  isi  scopus
    4. Rozikov U.A., “Gibbs Measures on Cayley Trees: Results and Open Problems”, Rev. Math. Phys., 25:1 (2013), 1330001  crossref  mathscinet  isi  elib  scopus
    5. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. 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  crossref  mathscinet  isi  scopus
    7. 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  crossref  mathscinet  isi  scopus
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