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A general compactness result and its application to the two-scale convergence of almost periodic functions. (English. Abridged French version) Zbl 0865.46003

Summary: We present a new general compactness result. This can be viewed as a generalization of the fact that the unit ball of a Hilbert space is weakly compact. Some consequences are Nguetseng’s result on the two-scale convergence of periodic functions and a similar (and new) result for almost periodic functions.

MSC:

46A50 Compactness in topological linear spaces; angelic spaces, etc.
42A75 Classical almost periodic functions, mean periodic functions
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