New development theory on measure pseudo-asymptotically omega periodic functions. (English) Zbl 1504.43006
Summary: The main goal of the paper concerns two parts, in the first one, we extend some results from J. Blot et al. [Decis. Econ. Finance 27, No. 1, 1–34 (2004; Zbl 1091.91053)] under general hypothesis on the measure, in the second part, we introduce a new class of functions, which we call measure pseudo \(\mathcal{S}\)-asymptotically omega periodic functions. The obtained results is the extension of those established recently in the literature. Then we establish many interesting results on those functions, namely their characterization, we give also several properties of those class of functions as composition results, the invariance by translation, and the convolution product. All sections are illustrated by examples or counter examples.
MSC:
| 43A60 | Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions |
| 34C27 | Almost and pseudo-almost periodic solutions to ordinary differential equations |
| 42A75 | Classical almost periodic functions, mean periodic functions |
Keywords:
measure ergodic function; characterization; measure pseudo \(\mathcal{S}\) asymptotically omega periodic function; convolution; translation invariance; completenessCitations:
Zbl 1091.91053References:
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