ALMOST PERIODIC FUNCTIONS AND FUNCTIONA - AMERIO L.

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Résumé :
The theory of almost-periodic functions with complex values, created by H. Bohr [1] in his two classical papers published in Acta Mathematica in 1925 and 1926, has been developed by many authors and has had note? worthy applications: we recall the works of Weyl, De la Vallee Poussin, Bochner, Stepanov, Wiener, Besicovic, Favard, Delsarte, Maak, Bogoliu? bov, Levitan. This subject has been widely treated in the monographs by Bohr [2], Favard [1], Besicovic [1], Maak [1], Levitan [1], Cinquini [1], Corduneanu [1], [2]. An important class of almost-periodic functions was studied at the beginning of the century by Bohl and Esclangon. Bohr's theory has been extended by Muckenhoupt [1] in a particular case and, subsequently, by Bochner [1] and by Bochner and Von Neumann [1] to very general abstract spaces. The extension to Banach spaces is, in particular, of great interest, in view of the fundamental importance of these spaces in theory and application.

Sommaire:
Theory of Almost-Periodic Functions.- Almost-Periodic Functions in Banach Spaces.- Harmonic Analysis of Almost-Periodic Functions.- Weakly Almost-Periodic Functions.- The Integration of Almost-Periodic Functions.- Applications to Almost-Periodic Functional Equations.- The Wave Equation.- The SchrÖdinger Type Equation.- The Wave Equation with Nonlinear Dissipative Term.- Results Regarding other Functional Equations.