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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
Received: 21.09.1982

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}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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