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Feynman formulae for Feller semigroups
Doklady Mathematics. 2010. Vol. 82. No. 2. P. 697–683.
Butko Ya. A., Schilling R. L., Smolyanov O.
Butko Ya. A., Grothaus M., Smolyanov O., Doklady Mathematics 2008 Vol. 78 No. 1 P. 590–595
Added: September 23, 2026
Butko Ya. A., Grothaus M., Smolyanov O., Infinite Dimensional Analysis, Quantum Probability and Related Topics 2010 Vol. 13 No. 3 P. 377–392
In this note a class of second-order parabolic equations with variable coefficients, depending on coordinate, is considered in bounded and unbounded domains. Solutions of the Cauchy–Dirichlet and the Cauchy problems are represented in the form of a limit of finite-dimensional integrals of elementary functions (such representations are called Feynman formulas). Finite-dimensional integrals in the Feynman formulas give approximations for functional integrals in the corresponding Feynman–Kac formulas, representing solutions of these ...
Added: September 22, 2026
Butko Ya. A., Schilling R. L., Smolyanov O., International Journal of Theoretical Physics 2011 Vol. 50 P. 2009–2018
A Feynman formula is a representation of the semigroup, generated by an initial-boundary value problem for some evolutionary equation, by a limit of integrals over Cartesian powers of some space E, the integrands being some elementary functions. The multiple integrals in Feynman formulae approximate integrals with respect to some measures or pseudomeasures on sets of functions ...
Added: September 22, 2026
Butko Ya. A., Böttcher B., Schilling R. L. et al., Russian Journal of Mathematical Physics 2011 Vol. 18 No. 4 P. 387–399
This note is devoted to Feynman formulas (i.e., representations of semigroups by limits of n-fold iterated integrals as n → ∞) and their connections with phase space Feynman path integrals. Some pseudodifferential operators corresponding to different types of quantization of a quadratic Hamiltonian function are considered. Lagrangian and Hamiltonian Feynman formulas for semigroups generated by these operators are ...
Added: September 22, 2026
Butko Ya. A., Schilling R. L., Smolyanov O., Infinite Dimensional Analysis, Quantum Probability and Related Topics 2012 Vol. 15 No. 3
A Feynman formula is a representation of a solution of an initial (or initial-boundary) value problem for an evolution equation (or, equivalently, a representation of the semigroup resolving the problem) by a limit of n-fold iterated integrals of some elementary functions as n → ∞. In this note we obtain some Feynman formulae for a class of semigroups associated with Feller processes. Finite-dimensional integrals in the Feynman formulae give approximations ...
Added: September 22, 2026
Butko Ya. A., Grothaus M., Smolyanov O., Journal of Mathematical Physics 2016 Vol. 57
Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. ...
Added: September 22, 2026
Olshanski G., Advances in Mathematics 2016 Vol. 300 P. 544–615
The paper consists of two parts. The first part introduces the representation ring for the family of compact unitary groups U(1), U(2), .... This novel object is a commutative graded algebra R with infinite-dimensional homogeneous components. It plays the role of the algebra of symmetric functions, which serves as the representation ring for the family ...
Added: December 2, 2016
Borodin A., Olshanski G., Electronic Journal of Probability 2013 Vol. 75 P. 1–43
The Thoma cone is an infinite-dimensional locally compact space, which is closely related to the space of extremal characters of the infinite symmetric group. In another context, the Thoma cone appears as the set of parameters for totally positive, upper triangular Toeplitz matrices of infinite size.
The purpose of the paper is to construct a family ...
Added: November 16, 2013