Skip to main content
Log in

Subharmonic functions on a directed graph

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. A. N. Kolmogorov, “Markov chains with a countable set of possible states,” Byull. Mosk. Un-ta (A),1, No. 3 (1937).

  2. V. I. romanovskii, Discrete Markov Chains [in Russian], Gostekhizdat, Moscow (1953).

    Google Scholar 

  3. W. R. Ashby, An Introduction to Cybernetics, Chapman and Hall, London (1956).

    Google Scholar 

  4. F. R. Gantmakher, Theory of Matrices [in Russian], Gostekhizdat, Moscow (1953).

    Google Scholar 

  5. J. Marik and V. Ptak, “Norms, spectra, and combinatorial properties of matrices,” Czech. Math. J.,10, No. 2, 181–196 (1960).

    Google Scholar 

  6. I. S. Berezin and N. P. Zhidkov, Computational Methods [in Russian], Vol. II, Fizmatgiz, Moscow (1959).

    Google Scholar 

  7. O. Taussky, “A recurring theorem of determinants,” Am. Math. Monthly,56, 672–676 (1949).

    Google Scholar 

  8. L. Collatz, “Über die konvergenzkriterien bei iterations verfahren für lineare gleichungssysteme,” Math. Zeitschr.,53, No. 2, 149–161 (1950).

    Google Scholar 

  9. V. Ptak and J. Sedlacek, “On the primitivity index of nonnegative matrices,” Czech. Math. J.,8, No. 4, 496–501 (1958).

    Google Scholar 

Download references

Authors

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 10, No. 3, May–June, pp. 600–613, 1969

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lyubich, Y.I., Tabachnikov, M.I. Subharmonic functions on a directed graph. Sib Math J 10, 432–442 (1969). https://doi.org/10.1007/BF01078333

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01078333

Keywords

Navigation