Electron. J. Diff. Eqns., Vol. 2002(2002), No. 70, pp. 1-15.

A spectral mapping theorem for evolution semigroups on asymptotically almost periodic functions defined on the half line

Constantin Buse

We prove that the evolution semigroup on $AAP_0(\mathbb{R}_+, X)$ is strongly continuous. Then we prove some properties of the generator of this evolution semigroup and show some applications in the theory of inequalities.

Submitted April 02, 2002. Published July 25, 2002.
Math Subject Classifications: 47G10, 47D03, 47A63.
Key Words: periodic families, almost periodic functions, exponential stability.

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Constantin Buse
Department of Mathematics
West University of Timisoara
Bd. V. Parvan 4
1900 Timisoara, Romania
e-mail: buse@hilbert.math.uvt.ro

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