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Composition of pseudo almost automorphic and asymptotically almost automorphic functions. (English) Zbl 1134.43001

Almost automorphic (AA) functions on the real line R with values in a Banach space X were originally defined by S. Bochner [Proc. Natl. Acad. Sci. USA 52, 907–910 (1964; Zbl 0134.30102)]. The present authors define several classes of functions including: (1) almost automorphic functions from \(R\times X\) into \(X\); (2) Co\((R, X)\) functions from \(R\) to \(X\) vanishing at infinity; (3) bounded continuous functions with vanishing mean value, AAo\((R, X)\); (4) asymptotically AA functions, AAA\((R, X)\); and (5) pseudo almost automorphic functions PAA\((R, X)\). The main theorems give conditions under which a composition of an AAA\((R \times X , X)\) function with another is again AAA, and under which a composition of a PAA\((R \times X , X)\) function with another is again PAA.

MSC:

43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions

Citations:

Zbl 0134.30102
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References:

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