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Feynman Formulas Representation of Semigroups Generated by Parabolic Difference-Differential Equations
Moscow Institute of Physics and Technology, People’s Friendship University of Russia, Moscow, Russia
Moscow Institute of Physics and Technology, People’s Friendship University of Russia, Moscow, Russia
- 1 Moscow Institute of Physics and Technology, People’s Friendship University of Russia, Moscow, Russia
- 2 Moscow Institute of Physics and Technology, People’s Friendship University of Russia, Moscow, Russia
American Journal of Computational Mathematics·Volume 02 (2012)·Pages 295–301·Published 18 December 2012·DOI10.4236/ajcm.2012.24040
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Abstract
We establish that the Laplas operator with perturbation by symmetrised linear hall of displacement argument operators is the generator of unitary group in the Hilbert space of square integrable functions. The representation of semigroup of Cauchy problem solutions for considered functional differential equation is given by the Feynman formulas.
KeywordsDifference-Differential EquationsSemigroupFeynman FormulaChernoff Theorem
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