Abstract
It is proved that the limit
, wheref: ℝ → ℝ is a locally integrable (in the sense of Lebesgue) function with zero mean and the supremum is taken over all solutions of the generalized differential equation γ ∈ [ω1, ω2], coincides with the limit
, where
. Here ¯λf = λf /T, ¯ If =If/T, and λf is the Lebesgue measure of the set
. It is established that this limit always exists for almost-periodic functionsf.
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Translated fromMatematicheskie Zametki, Vol. 59, No. 5, pp. 759–767, May, 1996.
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Filatov, O.P. Evaluation of the limits of maximal means. Math Notes 59, 547–553 (1996). https://doi.org/10.1007/BF02308823
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DOI: https://doi.org/10.1007/BF02308823