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

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.

Keywords

• Periodic evolution families
• uniform exponential stability
• boundedness
• evolution semigroup
• almost periodic functions