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

Abdelaziz Tajmouati; Abdeslam El Bakkali; Mohamed Baba Mohamed Ahmed

doi:10.5269/bspm.v38i5.40392

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

Abdelaziz Tajmouati Sidi Mohamed Ben Abdellah University
Abdeslam El Bakkali Chouaib Doukkali University
Mohamed Baba Mohamed Ahmed Sidi Mohammed Ben Abdellah University

DOI: https://doi.org/10.5269/bspm.v38i5.40392

Keywords: $\alpha$-times integrated semigroup, descent, ascent, Fredholm operator, Browder operator, Drazin invertible

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.