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.