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Composition of pseudo almost periodic and pseudo almost automorphic functions and applications to evolution equations. (English) Zbl 1186.43008
A bounded and continuous function f on the real line with values in a Banach space is a pseudo almost periodic function if it can be represented as f=g+h, where g is almost periodic and h satisfies lim |r| -r r h(t)dt=0. In the same way, the definition of pseudo almost automorphic functions is given. In this paper the authors study sufficient conditions for several composition operators to map a pseudo almost periodic function to a pseudo almost periodic function, or a pseudo almost automorphic function to a pseudo almost automorphic function. The results are then applied to the heat equation.
MSC:
43A60Almost periodic functions on groups, etc.; almost automorphic functions
34C27Almost and pseudo-almost periodic solutions of ODE