Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 19 (2024), 79 -- 107

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ALMOST PERIODIC AND QUASI-PERIODIC FUNCTIONS. A BRIEF SURVEY AND SOME APPLICATIONS.

Dhaou Lassoued

Abstract. In the present work, we study almost-periodic and quasi-periodic functions, their main properties and some related results. We also present almost periodic functions with parameters, which we adapt to the quasi-periodic framework. We then show that these spaces are isomorphic to other spaces of almost periodic functions (or quasi-periodic functions) with values in Banach spaces. We shall study in particular the superposition operators between these spaces. We introduce then a Sobolev-like space of almost periodic functions and analyze its main properties. We illustrate by some applications especially on convolution operation and almost periodic solutions of linear differential equations

2020 Mathematics Subject Classification: 42A75
Keywords: almost periodic functions; Sobolev-like space; Nemytskii operators

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Dhaou Lassoued
University of Gabès, Faculty of Sciences of Gabè
Department of Mathematics,
Mathematics and Applications Laboratory LR17ES11
Tunisia.
e-mail: Dhaou.Lassoued@fsg.rnu.tn, dhaou06@gmail.com

https://www.utgjiu.ro/math/sma