Spectral mapping theorems of differentiable C0 semigroups

2018/11/05 by Tajmouati, Abdelaziz, Boua, Hamid, Karmouni, Mohammed
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1811.01876

Abstract

Let (T(t))_{t≥ 0} be a C₀ 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∈σ_*(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 C₀ semigroup (T(t))_t≥0.

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