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On a module containment theorem of piecewise continuous almost periodic functions and its application. (English) Zbl 1389.42011

Summary: This paper is concentrated on giving a module containment theorem for piecewise continuous almost periodic functions (pcap function for short). One first analyses the relationship between the translation number set and some Fourier exponents of a pcap function. And then, combining with Kronecker’s theorem, a module containment theorem for a pcap function is established for the first time. As an application, the module structure of a pcap solution for an impulsive differential equation is characterized. Some remarks and a corollary are given to show the advantage of the module containment theorem.

MSC:

42A75 Classical almost periodic functions, mean periodic functions
34K14 Almost and pseudo-almost periodic solutions to functional-differential equations
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References:

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