Open AccessTHE THEOREM OF AVERAGING FOR THE ALMOST-PERIODIC FUNCTIONS
Author(s) -
О. П. Филатов
Publication year - 2012
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2012-18-6-100-112
Subject(s) - mathematics , mathematical analysis , limit (mathematics) , differential inclusion , spectrum (functional analysis) , space (punctuation) , convex hull , regular polygon , compact space , function (biology) , set (abstract data type) , variable (mathematics) , pure mathematics , combinatorics , geometry , physics , linguistics , philosophy , quantum mechanics , evolutionary biology , computer science , biology , programming language
It is proved that the limit of maximal mean is an independent variable of initial conditions if a vector exists from the convex hull of a compact set out of a nite-dimensional space and the components of vector are independent variables with respect to the spectrum of almost-periodic function. The compact set is the right hand of differential inclusion. The limit of maximal mean is taken over all solutions of the Couchy problem for the dierential inclusion.