Year: 2018
Type: preprint
Abstract: Let $(T(t))_{t\geq 0}$ be a $C_0$ semigroup on a Banach space $X$ with infinitesimal generator $A$. In this work, we give conditions for which the spectral mapping theorem $σ_{*}(T(t))\backslash \{0\}=\{e^{λs}, λ\inσ_{*}(A)\}$ holds, where $σ_*$ can be equal to the essential, Browder and Kato spectrum. Also, we will be interested in the relations between the spectrum of $A$ and the spectrum of the nth derivative $T(t)^{(n)}$ of a differentiable $C_0$ semigroup $(T(t))_{t\geq0}$.
Source: arXiv (Cornell University)
Institution: Cadi Ayyad University
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2899367246