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Zbl 1186.43008
Cieutat, Philippe; Fatajou, Samir; N'Guérékata, Gaston M.
Composition of pseudo almost periodic and pseudo almost automorphic functions and applications to evolution equations. (English)
[J] Appl. Anal. 89, No. 1, 11-27 (2010). ISSN 0003-6811; ISSN 1563-504X/e

A bounded and continuous function $f$ on the real line with values in a Banach space is a pseudo almost periodic function if it can be represented as $f= g+h,$ where $g$ is almost periodic and $h$ satisfies $\lim_{|r|\to \infty} \int^r_{-r}\| h(t)\|\,dt =0$. In the same way, the definition of pseudo almost automorphic functions is given. In this paper the authors study sufficient conditions for several composition operators to map a pseudo almost periodic function to a pseudo almost periodic function, or a pseudo almost automorphic function to a pseudo almost automorphic function. The results are then applied to the heat equation.
[Nguyen Van Minh (Carrollton)]

MSC 2000:: *43A60 Almost periodic functions on groups, etc.
34C27 Almost periodic solutions of ODE

Keywords: pseudo almost periodic function; pseudo almost automorphic function; evolution equation

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