Geodesic
Functionals for the~means of observables for one-dimensional infinite-particle systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 162 (2010) no. 3, pp. 422-438

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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, means of observables.
Mots-clés : cumulant (semi-invariant) 
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     author = {T. V. Ryabukha},
     title = {Functionals for the~means of observables for one-dimensional infinite-particle systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
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T. V. Ryabukha. Functionals for the~means of observables for one-dimensional infinite-particle systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 162 (2010) no. 3, pp. 422-438. http://geodesic.mathdoc.fr/item/TMF_2010_162_3_a7/