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 Izv. Akad. Nauk SSSR Ser. Mat., 1983, Volume 47, Issue 6, Pages 1162–1181 (Mi izv1441)

On the absence of exact means for some bounded functions

I. N. Blinov

Abstract: It is shown that there exist almost periodic functions $f(t)$ such that the function
$$\varphi(t)=\frac1{c+\int^t_0f(t) dt}$$
is bounded but does not have an exact mean value. This fact implies that there are first-order Bernoulli differential equations with almost periodic coefficients such that some bounded solutions do not have exact mean values.
Bibliography: 2 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1984, 23:3, 431–447

Bibliographic databases:

UDC: 517.9
MSC: Primary 42A75, 34C28; Secondary 34C27

Citation: I. N. Blinov, “On the absence of exact means for some bounded functions”, Izv. Akad. Nauk SSSR Ser. Mat., 47:6 (1983), 1162–1181; Math. USSR-Izv., 23:3 (1984), 431–447

Citation in format AMSBIB
\Bibitem{Bli83} \by I.~N.~Blinov \paper On the absence of exact means for some bounded functions \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1983 \vol 47 \issue 6 \pages 1162--1181 \mathnet{http://mi.mathnet.ru/izv1441} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=727750} \zmath{https://zbmath.org/?q=an:0566.43008|0537.43021} \transl \jour Math. USSR-Izv. \yr 1984 \vol 23 \issue 3 \pages 431--447 \crossref{https://doi.org/10.1070/IM1984v023n03ABEH001779}