European Workshop "Nonlinear Maps and Applications" - 2017, Nizhni Novgorod, Russia

Regular European Workshops "Nonlinear Maps and Applications" (NOMA) are held biannually in those European Universities where successful researchers in the area of nonlinear maps and their applications work. In far 1973 year French scientist Christian Mira organized Colloquium "Point Mappings and Applications" in the University of Toulouse, where he worked. According to Christian Mira, his mathematical preferences were formed under the influence of works of the founder of the Nizhni Novgorod nonlinear oscillations school A.A. Andronov

Unbounded random operators and Feynman formulae

We introduce and study probabilistic interpolations of various quantization methods. To do this, we develop a method for finding the expectations of unbounded random operators on a Hilbert space by averaging (with the help of Feynman formulae) the random one-parameter semigroups generated by these operators (the usual method for finding the expectations of bounded random operators is generally inapplicable to unbounded ones). Although the averaging of families of semigroups generates a function that need not possess the semigroup property, the Chernoff iterates of this function approximate a certain semigroup, whose generator is taken for the expectation of the original random operator. In the case of bounded random operators, this expectation coincides with the ordinary one. © 2016 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd

Unbounded random operators and Feynman formulae

We introduce and study probabilistic interpolations of various quantization methods. To do this, we develop a method for finding the expectations of unbounded random operators on a Hilbert space by averaging (with the help of Feynman formulae) the random one-parameter semigroups generated by these operators (the usual method for finding the expectations of bounded random operators is generally inapplicable to unbounded ones). Although the averaging of families of semigroups generates a function that need not possess the semigroup property, the Chernoff iterates of this function approximate a certain semigroup, whose generator is taken for the expectation of the original random operator. In the case of bounded random operators, this expectation coincides with the ordinary one. © 2016 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd

Averaging of random semigroups and quantization

Abstract: The properties of mean values of random variable with values in the set of semigroups of unitary operators are investigated. The mean value of random semigroup has no semigroup property. But it is equivalent in Chernoff sense to the semigroup with generator which is the result of averaging of generators of values of random semigroup. The problem of ambiguity of quantization of Hamiltonian systems is studied by using of semigroup averaging procedure.In particular the wide class of Shchrodinger operators on the graph is described by using of semigropus averaging procedure. The equivalence of presentation of quantum dynamics by unitary semigroup and by pseudomeasure on the space of trajectories of classical system is proved. The properties of averaging of random measures and random pseudomeasures (in particular, the linear and non-linear functionals on the space of measures and pseudomeasures) are studied.Note: Research direction:Mathematical modelling in actual problems of science and technic