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Éléments d'une construction axiomatique de la théorie des fonctions presque périodiques

Constantin Corduneanu


This paper presents an axiomatic approach for the construction of spaces of almost periodic functions (Poincar\'e, Bohr, Besicovitch \cite{2}  and \cite{3}; all these spaces are classical in the theory of almost periodic functions). Other known spaces, like Stepanov's or Weyl's, could be also treated in this framework. But Stepanov's space is part of Besicovitch's, while Weyl's space does not appear in applications (mechanics, physics etc.), to the best of our knowledge. This approach to oscillation theory is applicable in more general cases than almost periodicity, as indicated in our paper [8]. The space constructed there is more general than other spaces of oscillatory functions (for instance, the spaces of Osipov, V.F. or Zhang Chuanyi, also in the list of references). Our approach, which also relies on principles of functional analysis, establishes a more direct connection between function and associated series, than in the
classical framework. This fact is illustrated by some applications to functional equations in several papers of this author and his former students Y. Li and Mehran Mahdavi.


Almost periodic functions; Formal series; Funcional equations; Axiomaic theory

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