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On Beurling's inequality in terms of thermal power

Published online by Cambridge University Press:  14 July 2016

S. Kalpazidou
S. Kalpazidou*
Affiliation:
Aristotle University of Thessaloniki
*
∗Postal address: Aristotle University, Faculty of Sciences, Department of Mathematics, 54006 Thessaloniki, Greece.
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Abstract

Beurling's inequality is proved to have an interpretation in terms of ingredients that do not depend on the effective numerical contribution of transition probabilities of circuit processes (those processes whose transition law is expressed by a denumerable class of directed weighted circuits). Connections with reversibility for Sk-state, k≧2, circuit processes, where S is a denumerable set, are revealed.

Keywords

FLOWGROWTH FUNCTIONSYMMETRIC REVERSIBILITYCIRCUIT PROCESSES
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 1 , March 1991 , pp. 104 - 115
Copyright
Copyright © Applied Probability Trust 1991 

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References

[1] Beurling, A. and Deny, J. (1959) Dirichlet spaces. Proc. Nat. Acad. Sci. U.S.A. 45, 208–215.Google Scholar
[2] Chung, K. L. (1982) Lectures from Markov Processes to Brownian Motion. Springer-Verlag, New York.Google Scholar
[3] Iosifescu, M. (1973) On multiple Markovian dependence. Proc. 4th Conf. on Probability Theory, Brasov, 1971, Publishing House of the Romanian Academy, Bucharest, 65–71.Google Scholar
[4] Iosifescu, M. (1969) Sur les chaînes de Markov multiples. Bull. Inst. Internat. Statist. 43 (2), 333–335.Google Scholar
[5] Kalpazidou, S. (1988) On the representation of finite multiple Markov chains by weighted circuits. J. Multivariate Anal. 25, 241–271.Google Scholar
[6] Kalpazidou, S. (1989) On multiple circuit chains with a countable infinity of states. Stoch. Proc. Appl. 31, 51–70.CrossRefGoogle Scholar
[7] Kalpazidou, S. (1990) On reversible multiple Markov chains, Rev. Roumaine Math. Pures Appl. 35 (7).Google Scholar
[8] Lyons, T. (1983) A simple criterion for transience of a reversible Markov chain. Ann. Prob. 10, 393–402.Google Scholar
[9] Nash-Williams, C. St. J. A. (1959) Random walk and electric current in networks. Proc. Camb. Phil. Soc. 55, 181–194.Google Scholar
[10] Royden, H. L. (1952) Harmonic functions on open Riemann surfaces. Trans. Amer. Math. Soc. 75, 40–94.Google Scholar
[11] Thomson, W. and Tait, P. G. (1879) Treatise on Natural Philosophy. Cambridge University Press.Google Scholar
[12] Varopoulos, N. Th. (1984) Chaînes de Markov et inégalités isopérimétriques. C. R. Acad. Sci. Paris A298, 233–236.Google Scholar
[13] Varopoulos, N. Th. (1984) Isoperimetric inequalities and Markov chains. J. Functional Anal. 63, 215–239.Google Scholar