Geodesic
A new proof and generalization of the Bogolyubov–Ruelle theorem
Teoretičeskaâ i matematičeskaâ fizika, Tome 51 (1982) no. 3, pp. 389-402 Cet article a éte moissonné depuis la source Math-Net.Ru

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A new proof of the Bogolyubov–Ruelte theorem based on the general properties of a dual pair of Banach spaces $\langle'E_\xi, E_\xi\rangle$ is proposed. The new proof makes it possible to Lake into account readily the case of nonempty boundary conditions and extend the assertion of the theorem to a domain which includes the standard disk of analyticity with respect to the activity. 
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     title = {A~new proof and generalization of the {Bogolyubov{\textendash}Ruelle} theorem},
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V. A. Zagrebnov. A new proof and generalization of the Bogolyubov–Ruelle theorem. Teoretičeskaâ i matematičeskaâ fizika, Tome 51 (1982) no. 3, pp. 389-402. http://geodesic.mathdoc.fr/item/TMF_1982_51_3_a9/

[1] Bogolyubov N. N., Khatset B. I., DAN SSSR, 66:3 (1949), 321–324 ; Боголюбов Н. Н., Избранные труды в трех томах, т. 2, Наукова думка, Киев, 1970, 494–498 | MR | Zbl | MR

[2] Ruelle D., Ann. of Phys., 25:1 (1963), 109–120 | DOI | MR

[3] Ryuel D., Statisticheskaya mekhanika. Strogie rezultaty, Mir, M., 1971

[4] Bogolyubov N. N., Petrina D. Ya., Khatset B. I., TMF, 1:2 (1969), 251–274 | MR

[5] Simyatitskii I. L., TMF, 6:2 (1971), 230–237

[6] Minlos R. A., Funkts. analiz i ego prilozh., 1:2 (1967), 60–73 | MR | Zbl

[7] Ruelle D., J. Math. Phys., 8:8 (1967), 1657–1668 | DOI | MR | Zbl

[8] Dobrushin R. L., Teoriya veroyatn. i ee primen., 13:2 (1968), 201–229 | MR

[9] Dobrushin R. L., Funkts. analiz i ego prilozh., 3:1 (1969), 27–35 ; Добрушин Р. Л., ТМФ, 4:1 (1970), 101–118 | MR | Zbl | MR | Zbl

[10] Lanford III O. E., Ruelle D., Commun. Math. Phys., 13:3 (1969), 194–215 | DOI | MR

[11] Minlos R. A., UMN, 23:1 (1963), 133–190 ; Теория фазовых переходов. Строгие результаты, гл. 1, Наука, М., 1980 | MR | MR

[12] Nazin G. I., DAN SSSR, 245:6 (1979), 1352–1355 ; ТМФ, 42:3 (1980), 383–391 ; 2, 243–252 | MR | MR | MR

[13] Bogolyubov N. N., Problemy dinamicheskoi teorii v statisticheskoi fizike, GITTL, M.–L., 1946 | MR

[14] Dobrushin R. L., Funkts. analiz i ego prilozh., 2:4 (1968), 44–57 ; Теория вероятн. и ее примен., 15:3 (1970), 469–497 | MR | Zbl | Zbl

[15] Lanford III O. E., “Entropy and Equilibrium States in Classical Statistical Mechanics”, Lecture Notes in Physics, 20, Springer, Berlin–Heidelberg–N.-Y., 1973, 1–113 ; Simon B., Commun. Math. Phys., 68:2 (1979), 183–185 | DOI | DOI | MR | Zbl

[16] Zagrebnov V. A., Preprint R5-80-458, OIYaI, Dubna, 1980

[17] Penrose O., J. Math. Phys., 4:10 (1963), 1312–1320 | DOI | MR | Zbl

[18] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1972 | MR

[19] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, t. 1: Funktsionalnyi analiz, Mir, M., 1977 | MR

[20] Danford N., Shvarts Dzh. T., Lineinye operatory. Obschaya teoriya, IL, M., 1962 | MR

[21] Gurevich B. M., Suchov Ju. M., Commun. Math. Phys., 49:1 (1976), 63–96 ; Aizenmann M., Goldstein S., Lebowitz J. L., Commun. Math. Phys., 62:3 (1978), 279–302 | DOI | MR | DOI | MR

[22] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl

[23] Ruelle D., Commun. Math. Phys., 18:2 (1970), 127–159 | DOI | MR | Zbl

[24] Zagrebnov V. A,, Pastur L. A., TMF, 36:3 (1978), 352–372 | MR

[25] Gibbsovskie sostoyaniya v statisticheskoi fizike, Sbornik statei. Perevod s angl., ed. R. A. Minlos, Mir, M., 1978 | MR

[26] Malyshev V. A., TMF, 45:2 (1980), 235–243 | MR

[27] Gruber C., Lebowitz J. L., Commun. Math. Phys., 41:1 (1975), 11–18 | DOI | MR

[28] Fröhlich J., Park Y. M., Commun. Math. Phys., 59:3 (1978), 235–266 | DOI | MR