SUR LE CRITÈRE DE LA PRESQUE PÉRIODICITÉ DE BOCHNER

We give an extension of Bochner's criterion for the almost periodic functions. By using our main result, we extend two results of A. Haraux. The first is a generalization of Bochner's criterion which is useful for periodic dynamical systems. The second is a characterization of periodic functions in term of Bochner's criterion.Nous donnons une extension du critère de Bochner pour les fonctions presque périodiques. En utilisant notre résultat principal, nous prolongeons deux résultats de A. Haraux. Le premier est une généralisation du critère de Bochner qui est utile pour les systèmes dynamiques périodiques. La seconde est une caractérisation des fonctions périodiques en terme de critère de Bochner

NEMYTSKII OPERATORS BETWEEN STEPANOV ALMOST PERIODIC OR ALMOST AUTOMORPHIC FUNCTION SPACES

We study the superposition operators (also called Nemytskii operators) between spaces of almost periodic (respectively almost automorphic) functions in the sense of Stepanov. We state new results on the superposition, notably we give a necessary and sufficient condition for that these operators are well-defined and continuous. 2010 Mathematic Subject Classification: Superposition operators, Stepanov almost periodic functions, Stepanov almost automorphic functions, Bochner transform

Maximum principle and existence of almost-periodic solutions of second-order differential systems

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