| Autor: |
Orlov, Yu. N., Sakbaev, V. Z. |
| Zdroj: |
Lobachevskii Journal of Mathematics; Jun2024, Vol. 45 Issue 6, p2567-2576, 10p |
| Abstrakt: |
We study the bijection of the space of one-parameter families of bounded linear operators in a space of functions on a coordinate space onto the set of complex-valued finitely additive cylindrical measures in the space of trajectories in the coordinate space. From the space of measures on the space of trajectories, a set of measures representing semigroups is distinguished. A procedure is defined for constructing Feynman measures on the space of trajectories representing semigroups generated by a linear functional differential equation with delay. Using the Feynman–Kac formulas and a measure on the space of trajectories corresponding to an unperturbed semigroup, the perturbation of a semigroup by a bounded potential on the space of trajectory values is studied. A perturbed semigroup is defined by integrating the perturbation functional on the trajectory space over the Feynman cylindrical measure corresponding to the unperturbed semigroup. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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