Abstract
A periodic evolutionary process {U(t,s)}t≥s with period τ on a Banach space X gives an evolution semigroup with the generator L on the space of τ-periodic continuous X-valued functions. We prove that the generalized eigenspaces NL=N((αI−L)n) and NU=N((eατI−U(τ,0))n) are isomorphic. The algebraic representation of a function u∈NL is given by the initial value u(0)=w∈NU.
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