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On a module containment theorem of piecewise continuous almost periodic functions and its application

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Abstract

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.

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Authors and Affiliations

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, P. R. China

    L. Wang

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  1. L. Wang
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Correspondence to L. Wang.

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This work was supported by the Fundamental Research Funds for the Central Universities (3102014JC-Q01087).

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Wang, L. On a module containment theorem of piecewise continuous almost periodic functions and its application. Anal Math 42, 387–400 (2016). https://doi.org/10.1007/s10476-016-0406-4

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  • DOI: https://doi.org/10.1007/s10476-016-0406-4

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