Some Properties of Functional Integrals with Respect to the Bogoliubov Measure

被引：0
作者：
D. P. Sankovich
机构：
[1] Steklov Institute of Mathematics,
[2] RAS,undefined
来源：
Theoretical and Mathematical Physics | 2001年 / 126卷
关键词：
Continuous Function; Broad Class; Nonlinear Oscillator; Approximate Formula; Functional Integral;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
引用
收藏
页码：121 / 135
页数：14
相关论文
共 32 条
[21]   Reduction of a Functional Integral over Discontinuous Trajectories to Integrals over Continuous Trajectories [J].
Kolpakov, E. S. .
MOSCOW UNIVERSITY MATHEMATICS BULLETIN, 2021, 76 (04) :168-171
[22]   Some applications of simultaneous continuous functional calculus [J].
M. Mazighi ;
A. El Kinani .
Rendiconti del Circolo Matematico di Palermo Series 2, 2023, 72 :1629-1638
[23]   Some applications of simultaneous continuous functional calculus [J].
Mazighi, M. ;
El Kinani, A. .
RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2023, 72 (03) :1629-1638
[24]   On some properties of the space of upper semicontinuous functions [J].
Osipov, A. V. ;
Pytkeev, E. G. .
ACTA MATHEMATICA HUNGARICA, 2019, 157 (02) :459-464
[25]   ON SOME PROPERTIES OF THE SUPERPOSITION OPERATOR ON TOPOLOGICAL MANIFOLDS [J].
Dronka, Janusz .
OPUSCULA MATHEMATICA, 2010, 30 (01) :69-77
[26]   On some properties of the space of upper semicontinuous functions [J].
A. V. Osipov ;
E. G. Pytkeev .
Acta Mathematica Hungarica, 2019, 157 :459-464
[27]   Properties of Some Overlapping Self-Similar and Some Self-Affine Measures [J].
J. Neunhauserer .
Acta Mathematica Hungarica, 2001, 92 :143-161
[28]   Some properties of nonlinear Volterra-Stieltjes integral operators [J].
Banas, J ;
Mena, JC .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2005, 49 (9-10) :1565-1573
[29]   SOME THEOREMS ON PASSING FROM LOCAL TO GLOBAL PRESENCE OF PROPERTIES OF FUNCTION [J].
Skordev, Dimiter .
LOGICAL METHODS IN COMPUTER SCIENCE, 2016, 12 (04) :1-11
[30]   Some nonlinear boundary value problems for a third-order functional-differential equation [J].
A. Ya. Lepin ;
L. A. Lepin ;
V. D. Ponomarev .
Differential Equations, 2007, 43 :1067-1071
1234