Add to ORKGAbstract: The averaging procedure of one-parametric semigroups, based on Chernoff equivalence for operator-functions is constructed. The initial problem solutions are investigated for fractional diffusion equation and for Schrödinger equation with relativistic Hamiltonian of freedom motion. It is established, that in these examples the quantization can be treated as averaging of random translation operators in classical coordinate space.Note: Research direction:Mathematical modelling in actual problems of science and technic
AbstractWe discuss the regularity of the oscillatory semigroup eitH, where H=-Δ+|x|2 is the n-dimens...
AbstractSuppose that α∈(0,2) and that X is an α-stable-like process on Rd. Let F be a function on Rd...
AbstractWe prove a Feynman–Kac formula for Schrödinger type operators on vector bundles over arbitra...
The extension of averaging procedure for operator-valued function is defined by means of the integra...
The extension of averaging procedure for operator-valued function is defined by means of the integra...
Abstract: The properties of mean values of random variable with values in the set of semig...
We introduce and study probabilistic interpolations of various quantization methods. To do this, we ...
AbstractWe study the generalized Schrödinger operator −L + V, where L is the generator of a symmetri...
AbstractWe study the generalized Schrödinger operator −L + V, where L is the generator of a symmetri...
The thesis presents a probabilistic approach to the theory of semigroups of operators, with particul...
Abstract: The system of ODE, which describes dynamics of quantum averages of operators of ...
The theory of one parameter semigroups of bounded linear operators on Banach spaces has deep and far...
AbstractIf the potential in a two-particle system is the boundary value of an analytic function, the...
An exact analogue of the method of averaging in classical mechanics is constructed for self--adjoint...
Many results, both from semigroup theory itself and from the applied sciences, are phrased in discip...
AbstractWe discuss the regularity of the oscillatory semigroup eitH, where H=-Δ+|x|2 is the n-dimens...
AbstractSuppose that α∈(0,2) and that X is an α-stable-like process on Rd. Let F be a function on Rd...
AbstractWe prove a Feynman–Kac formula for Schrödinger type operators on vector bundles over arbitra...
The extension of averaging procedure for operator-valued function is defined by means of the integra...
The extension of averaging procedure for operator-valued function is defined by means of the integra...
Abstract: The properties of mean values of random variable with values in the set of semig...
We introduce and study probabilistic interpolations of various quantization methods. To do this, we ...
AbstractWe study the generalized Schrödinger operator −L + V, where L is the generator of a symmetri...
AbstractWe study the generalized Schrödinger operator −L + V, where L is the generator of a symmetri...
The thesis presents a probabilistic approach to the theory of semigroups of operators, with particul...
Abstract: The system of ODE, which describes dynamics of quantum averages of operators of ...
The theory of one parameter semigroups of bounded linear operators on Banach spaces has deep and far...
AbstractIf the potential in a two-particle system is the boundary value of an analytic function, the...
An exact analogue of the method of averaging in classical mechanics is constructed for self--adjoint...
Many results, both from semigroup theory itself and from the applied sciences, are phrased in discip...
AbstractWe discuss the regularity of the oscillatory semigroup eitH, where H=-Δ+|x|2 is the n-dimens...
AbstractSuppose that α∈(0,2) and that X is an α-stable-like process on Rd. Let F be a function on Rd...
AbstractWe prove a Feynman–Kac formula for Schrödinger type operators on vector bundles over arbitra...