Kim, Dohan; Miyazaki, Rinko; Naito, Toshiki; Shin, Jong Son Normal eigenvalues in evolutionary process. (English) Zbl 1353.47079 J. Korean Math. Soc. 53, No. 4, 895-908 (2016). 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 \(X\). Cited in 2 Documents MSC: 47D06 One-parameter semigroups and linear evolution equations 47A10 Spectrum, resolvent 35K05 Heat equation Keywords:\(C_0\)-semigroup; evolution semigroup; monodromy operator; normal eigenvalue; order of pole; ascent PDFBibTeX XMLCite \textit{D. Kim} et al., J. Korean Math. Soc. 53, No. 4, 895--908 (2016; Zbl 1353.47079) Full Text: DOI Link