Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 175, pp. 1-9.

Title: Spectral mapping theorem for an evolution semigroup on a space
       of vector-valued almost-periodic functions

Author: Olivia Saierli (West Univ. of Timisoara, Romania)
         
Abstract:
 We give some characterizations for exponential stability of a periodic
 evolution family of bounded linear operators acting on a Banach
 space in terms of evolution semigroups acting on a special space of
 almost periodic functions. As a consequence, a spectral mapping
 theorem is stated.
 
Submitted May 11, 2012. Published October 12, 2012.
Math Subject Classifications: 47A05, 47A30, 47D06, 47A10, 35B15, 35B10.
Key Words: Periodic evolution families; uniform exponential stability;
           boundedness; evolution semigroup; almost periodic functions.