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Normal eigenvalues in evolutionary process. (English) Zbl 1353.47079

Summary: Firstly, we establish spectral mapping theorems for normal eigenvalues (due to Browder) of a \(C_0\)-semigroup and its generator. Secondly, we discuss relationships between normal eigenvalues of the compact monodromy operator and the generator of the evolution semigroup on \(P_\tau(X)\) associated with the \(\tau\)-periodic evolutionary process on a Banach space \(X\), where \(P_\tau(X)\) stands for the space of all \(\tau\)-periodic continuous functions mapping \(\mathbb R\) to \(X\).

MSC:

47D06 One-parameter semigroups and linear evolution equations
47A10 Spectrum, resolvent
35K05 Heat equation
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