Geodesic
Metric Properties of Bogoliubov Trajectories in Statistical Equilibrium Theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 1, pp. 125-142 
D. P. Sankovich. Metric Properties of Bogoliubov Trajectories in Statistical Equilibrium Theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 1, pp. 125-142. http://geodesic.mathdoc.fr/item/TMF_2001_127_1_a8/
@article{TMF_2001_127_1_a8,
     author = {D. P. Sankovich},
     title = {Metric {Properties} of {Bogoliubov} {Trajectories} in {Statistical} {Equilibrium} {Theory}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {125--142},
     year = {2001},
     volume = {127},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_127_1_a8/}
}
TY  - JOUR
AU  - D. P. Sankovich
TI  - Metric Properties of Bogoliubov Trajectories in Statistical Equilibrium Theory
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2001
SP  - 125
EP  - 142
VL  - 127
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2001_127_1_a8/
LA  - ru
ID  - TMF_2001_127_1_a8
ER  - 
%0 Journal Article
%A D. P. Sankovich
%T Metric Properties of Bogoliubov Trajectories in Statistical Equilibrium Theory
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2001
%P 125-142
%V 127
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2001_127_1_a8/
%G ru
%F TMF_2001_127_1_a8

Voir la notice de l'article provenant de la source Math-Net.Ru

We investigate some properties of the Bogoliubov measure that appear in statistical equilibrium theory for quantum systems and establish the nondifferentiability of the Bogoliubov trajectories in the corresponding function space. We prove a theorem on the quadratic variation of trajectories and study the properties implied by this theorem for the scale transformations. We construct some examples of semigroups related to the Bogoliubov measure. Independent increments are found for this measure. We consider the relation between the Bogoliubov measure and parabolic partial differential equations.

[1] N. N. Bogolyubov, DAN SSSR, 99 (1954), 225 | MR | Zbl

[2] D. P. Sankovich, TMF, 119 (1999), 345 | DOI | MR | Zbl

[3] G. W. Johnson, M. L. Lapidus, The Feynman Integral and Feynman's Operational Calculus, Clarendon Press, Oxford, 2000 | MR | Zbl

[4] H. L. Royden, Real Analysis, 3rd ed., Macmillan, NY, 1988 | MR | Zbl

[5] P. Lévy, Amer. J. Math., 62 (1940), 487 | DOI | MR | Zbl

[6] R. H. Cameron, W. T. Martin, Bull. Amer. Math. Soc., 53 (1947), 130 | DOI | MR | Zbl

[7] A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integraly i ryady. Elementarnye funktsii, Nauka, M., 1981 | MR | Zbl

[8] E. Khille, R. Fillips, Funktsionalnyi analiz i polugruppy, IL, M., 1962 | MR

[9] E. B. Davies, One-Parameter Semigroups, Academic Press, London, 1980 | MR | Zbl

[10] V. I. Bogachev, Gaussovskie mery, Nauka, M., 1997 | MR

[11] L. A. Yanovich, Priblizhennoe vychislenie kontinualnykh integralov po gaussovym meram, Nauka i tekhnika, Minsk, 1976 | MR | Zbl

[12] Kh.-S. Go, Gaussovskie mery v banakhovykh prostranstvakh, Mir, M., 1979