Normal eigenvalues in evolutionary process
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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 $X$.
Abstract
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 $X$.
참고문헌 (15)
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