Open AccessTHE THEOREM OF AVERAGING IN THE CONDITION OF UNLIMETED SPEED FOR ALMOST-PERIODIC FUNCTIONS
Author(s) -
О. П. Филатов
Publication year - 2013
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2013-19-3-53-57
Subject(s) - mathematics , differential inclusion , mathematical analysis , limit (mathematics) , differential (mechanical device) , convex hull , variable (mathematics) , regular polygon , function (biology) , periodic function , space (punctuation) , set (abstract data type) , geometry , physics , linguistics , philosophy , evolutionary biology , biology , computer science , thermodynamics , programming language
It is proved that the limit of maximal mean is an independent variable of initial conditions if an axis exists from the convex hull of a set of permitted speeds out of a finite-dimensional space and the components of direction vector of the axis are the independent variables with respect to a spectrum of almost-periodic function. The set of permitted speeds is the right hand of differential inclusion. The limit of maximal mean is taken over all solutions of the Couchy problem for the differential inclusion.