This article is cited in 2 papers

Functionals for the means of observables for one-dimensional infinite-particle systems

T. V. Ryabukha

Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine

Abstract: We study the problem of the existence of means of observables for infinite-particle systems. Using solutions of the Cauchy problems for the BBGKY hierarchy and for its dual, we prove the local existence in time of the mean-value functionals in the cases where either the observables or the states vary in time. We also discuss the problem of the existence of such functionals for several different classes of observables and for an arbitrary time interval.

Keywords: infinite-particle system, BBGKY hierarchy, dual BBGKY hierarchy, cumulant (semi-invariant), means of observables.

Received: 07.04.2009

DOI: 10.4213/tmf6480

 English version: Theoretical and Mathematical Physics, 2010, 162:3, 352–365

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