Almost periodic and quasi-periodic functions. A brief survey and some applications - Dhaou Lassoued (Surveys in Mathematics and its Applications, 2024)
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