This article is cited in 2 papers

Mathematics

The theorem of averaging for the almost-periodic functions

O. P. Filatov

The Dept. of Equations of Mathematical Physics, Samara State University, Samara, 443011, Russian Federation

Abstract: 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 finite-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 differential inclusion.

Keywords: limit of maximal mean, theorem of averaging, differential inclusion, compact right hand, almost-periodic function, independent frequencies with respect to spectrum.

UDC: 517.928.1

Received: 10.02.2012
Accepted: 10.02.2012