Spectral inclusions between $(\alpha+1)$-times integrated semigroups and its generators

Abstract

We interest to $\alpha$-times integrated semigroups that are the solution of the $(\alpha+1)$-times integrated Cauchy problems. Particulary, we characterize partially the different spectrums of $\alpha$-times integrated semigroups using the spectrums of its generators.

Keywords

• $\alpha$-times integrated semigroup
• descent
• ascent
• Fredholm operator
• Browder operator
• Drazin invertible