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Zbl 0901.42005
Zhang, Ch.
Vector-valued pseudo almost periodic functions. (English)
[J] Czech. Math. J. 47, No.3, 385-394 (1997). ISSN 0011-4642; ISSN 1572-9141/e

The author deals with a new generalization of (vector-valued) almost periodic functions to (vector-valued) pseudo almost periodic functions. Many well-known functions connected with the notion of almost periodic functions are contained as special cases in the class of these pseudo almost periodic functions. \par Definition 5 defines a pseudo periodic function using a generalized almost periodicity and a generalized uniform continuity. \par The pseudo almost periodic functions remind the former generalization of almost periodic functions to asymptotically almost periodic functions with their unique decomposition as a sum of an almost periodic function and a limit zero perturbation. The main result of this paper consists in Theorem 11 which shows that any pseudo almost periodic function has a unique decomposition as a sum of an almost periodic function and an ergodic perturbation. \par The interesting Example 14 illustrates the fact that the generalized almost periodicity of a pseudo almost periodic function does not guarantee its generalized uniform continuity. \par The space of pseudo almost periodic functions is a Banach space.
[A.Fischer (Praha)]

MSC 2000:: *42A75 Periodic functions and generalizations
43A60 Almost periodic functions on groups, etc.

Keywords: pseudo almost periodic functions; ergodic perturbation

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