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TMF, 2001, Volume 126, Number 1, Pages 149–163 (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

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.

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

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English version:
Theoretical and Mathematical Physics, 2001, 126:1, 121–135

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Received: 25.05.2000

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
\by D.~P.~Sankovich
\paper Some Properties of Functional Integrals with Respect to the Bogoliubov Measure
\jour TMF
\yr 2001
\vol 126
\issue 1
\pages 149--163
\jour Theoret. and Math. Phys.
\yr 2001
\vol 126
\issue 1
\pages 121--135

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    This publication is cited in the following articles:
    1. M. Corgini, D. P. Sankovich, “Local Gaussian Dominance: An Anharmonic Excitation of Free Bosons”, Theoret. and Math. Phys., 132:1 (2002), 1019–1028  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. D. P. Sankovich, “The Bogolyubov Functional Integral”, Proc. Steklov Inst. Math., 251 (2005), 213–245  mathnet  mathscinet  zmath
    3. V. R. Fatalov, “Some asymptotic formulas for the Bogoliubov Gaussian measure”, Theoret. and Math. Phys., 157:2 (2008), 1606–1625  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. 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  mathnet  crossref  crossref  adsnasa  isi
    5. V. R. Fatalov, “Laplace-type exact asymptotic formulas for the Bogoliubov Gaussian measure”, Theoret. and Math. Phys., 168:2 (2011), 1112–1149  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    6. 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  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    7. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    8. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. Lifshits M. Nazarov A., “L-2-Small Deviations For Weighted Stationary Processes”, Mathematika, 64:2 (2018), 387–405  crossref  mathscinet  zmath  isi
    10. Nazarov A.I. Nikitin Ya.Yu., “On Small Deviation Asymptotics in l-2 of Some Mixed Gaussian Processes”, 6, no. 4, 2018, 55  crossref  zmath  isi  scopus  scopus
    11. V. R. Fatalov, “Functional integrals for the Bogoliubov Gaussian measure: Exact asymptotic forms”, Theoret. and Math. Phys., 195:2 (2018), 641–657  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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