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• W2955272639 abstract "There is no uniform continuity property formulated in the Bohr’s definition of continuous almost periodic function. The property is a consequence of the definition and it is obtained as the theorem. Nevertheless, the property of conditional uniform continuity is assumed in the definition of the discontinuous almost periodic function. Thus, if one wants to follow the classical way of the theory construction, a new approach has to be found. Initial steps, and it seems still the last ones, for the task were done in our papers. On the basis of a special topology for the set of piecewise continuous functions a distance was utilized to define discontinuous almost periodic functions. Thus, the conditional uniform continuity and uniform almost periodicity for the derivative sequences are results of lemmas next to the definition. They are delivered in the first section of this chapter. In the second section we are concentrated on the Bochner definition of discontinuous almost periodic function. This was done in our papers for the first time. The Bochner’s definition is convenient for topological dynamics. Initially, the dynamics was applied either to autonomous equations or to non-autonomous periodic systems through the Poincare map. Through the approach the regularity of the linear discontinuous almost periodic operator has been proved. It is an extension of the result by Mukhmadiev. Moreover, impulsive versions of Amerio and Favard theorems are obtained as well as theorems concerning recurrent and limit almost periodic solutions." @default.
• W2955272639 created "2019-07-12" @default.
• W2955272639 creator A5004206574 @default.
• W2955272639 date "2019-06-21" @default.
• W2955272639 modified "2023-09-27" @default.
• W2955272639 title "Bohr and Bochner Discontinuities" @default.
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• W2955272639 doi "https://doi.org/10.1007/978-3-030-20572-0_5" @default.
• W2955272639 hasPublicationYear "2019" @default.
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