The base of the theory of measures on infinitely dimensional topological vector spaces is considered. The differential calculus for the measures on locally convex spaces is introduced. The above technique is used to obtain the presentation of solution of initial boundary value problem for an evolutionary equation by means of Feynman-Kac formulas. The approximations for a such solution by means of Feynman formulas are obtained. The properties of a measure to be absolutely continuous or singular with respect to another measure are considered. In particular, the invariance or quasi-invariance of a measure with respect to a group of transformations are studied. In addition, we consider the integration of a function with respect to finite additive measure and we study the properties of vector valued functions which is integrable by Pettis of by Bochner with respect to such a measure.

Fall Semester Schedule of 2021/2022:

Time: Tuesday 16:25 – 17:50

First lecture: September 7

Financial support. The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2019-1614).

Seminar organizers
Sakbaev Vsevolod Zhanovich
Smolyanov Oleg Georgievich

Organizations
Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center