caa a22 4500 475741722 CHVBK 20180406123501.0 cr unu---uuuuu 170329e20000301xx s 000 0 eng 10.1007/BF02676672 doi (NATIONALLICENCE)springer-10.1007/BF02676672 Filatov O. Samara State University, USSR aut Existence of limits of maximal means [Elektronische Daten] [O. Filatov] For the class II(ℝ m ) of continuous almost periodic functionsf: ℝ m → ℝ, we consider the problem of the existence of the limit 1 $$M_f = \mathop {\lim }\limits_{\Delta \to \infty } \mathop {\sup }\limits_\gamma \frac{1}{\Delta }\int_0^\Delta f (\gamma (t))dt$$ where the least upper bound is taken over all solutions (in the sense of Carathéodory) of the generalized differential equation {ie365-1} εG, γ(0)=a 0. We establish that if the compact setG ⊂ ℝ m is not contained in a subspace of ℝ m of dimensionm−1 (i.e., if it is nondegenerate), then the limit exists uniformly in the initial vectora 0 ε ℝ m . Conversely, if for any functionf ε π(ℝ m ), the limit exists uniformly in the initial vectora 0 ε ℝ m , then the compact setG is nondegenerate. We also prove that there exists an extremal solution for which a limit of the maximal mean uniform in the initial conditions is realized. Kluwer Academic/Plenum Publishers, 2000 almost periodic functions nationallicence maximal means nationallicence compact set nationallicence solutions in the sense of Carathéodory of generalized differential equations nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/3(2000-03-01), 365-371 0001-4346 67:3<365 2000 67 11006 https://doi.org/10.1007/BF02676672 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02676672 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Filatov O. Samara State University, USSR aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/3(2000-03-01), 365-371 0001-4346 67:3<365 2000 67 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer