D. P. Sankovich, “Some Properties of Functional Integrals with Respect to the Bogoliubov Measure”, TMF, 126:1 (2001), 149–163; Theoret. and Math. Phys., 126:1 (2001), 121

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Teoreticheskaya i Matematicheskaya Fizika, 2001, Volume 126, Number 1, Pages 149–163
DOI: https://doi.org/10.4213/tmf421 (Mi tmf421)

This article is cited in 11 scientific papers (total in 11 papers)

Some Properties of Functional Integrals with Respect to the Bogoliubov Measure

D. P. Sankovich

Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (269 kB) Citations (11)

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DOI: https://doi.org/10.4213/tmf421

Abstract: We consider problems related to integration with respect to the Bogoliubov measure in the space of continuous functions and calculate some functional integrals with respect to this measure. Approximate formulas that are exact for functional polynomials of a given degree and also some formulas that are exact for integrable functionals belonging to a broader class are constructed. An inequality for traces is proved, and an upper estimate is derived for the Gibbs equilibrium mean square of the coordinate operator in the case of a one-dimensional nonlinear oscillator with a positive symmetric interaction.

Received: 25.05.2000

English version:
Theoretical and Mathematical Physics, 2001, Volume 126, Issue 1, Pages 121–135
DOI: https://doi.org/10.1023/A:1005262400667

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: D. P. Sankovich, “Some Properties of Functional Integrals with Respect to the Bogoliubov Measure”, TMF, 126:1 (2001), 149–163; Theoret. and Math. Phys., 126:1 (2001), 121–135

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf421

https://doi.org/10.4213/tmf421

https://www.mathnet.ru/eng/tmf/v126/i1/p149

This publication is cited in the following 11 articles:

Lifshits M. Nazarov A., “L-2-Small Deviations For Weighted Stationary Processes”, Mathematika, 64:2 (2018), 387–405
Nazarov A.I. Nikitin Ya.Yu., “On Small Deviation Asymptotics in l-2 of Some Mixed Gaussian Processes”, 6, no. 4, 2018, 55
V. R. Fatalov, “Functional integrals for the Bogoliubov Gaussian measure: Exact asymptotic forms”, Theoret. and Math. Phys., 195:2 (2018), 641–657
V. R. Fatalov, “Exact Laplace-type asymptotic formulas for the Bogoliubov Gaussian measure: The set of minimum points of the action functional”, Theoret. and Math. Phys., 191:3 (2017), 870–885
Nazarov A.I., Sheipak I.A., “Degenerate self-similar measures, spectral asymptotics and small deviations of Gaussian processes”, Bull London Math Soc, 44:1 (2012), 12–24
V. R. Fatalov, “Asymptotic behavior of small deviations for Bogoliubov's Gaussian measure in the $L^p$ norm, $2\le p\le\infty$ ”, Theoret. and Math. Phys., 173:3 (2012), 1720–1733
V. R. Fatalov, “Laplace-type exact asymptotic formulas for the Bogoliubov Gaussian measure”, Theoret. and Math. Phys., 168:2 (2011), 1112–1149
R. S. Pusev, “Asymptotics of small deviations of the Bogoliubov processes with respect to a quadratic norm”, Theoret. and Math. Phys., 165:1 (2010), 1348–1357
V. R. Fatalov, “Some asymptotic formulas for the Bogoliubov Gaussian measure”, Theoret. and Math. Phys., 157:2 (2008), 1606–1625
D. P. Sankovich, “The Bogolyubov Functional Integral”, Proc. Steklov Inst. Math., 251 (2005), 213–245
M. Corgini, D. P. Sankovich, “Local Gaussian Dominance: An Anharmonic Excitation of Free Bosons”, Theoret. and Math. Phys., 132:1 (2002), 1019–1028

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	441
Full-text PDF :	214
References:	47
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