Quasi-fredholm and saphar spectrums for the {\alpha}-times integrated semigroups

TL;DR

This paper investigates the spectral properties of -times integrated semigroups, providing characterizations of various spectrum types like quasi-Fredholm and Saphar spectra through their generators.

Contribution

It offers new characterizations of multiple spectrum types for -times integrated semigroups based on their generators, extending existing spectral theory.

Findings

Characterization of quasi-Fredholm spectrum for -times integrated semigroups

Analysis of Saphar and essentially Saphar spectra in this context

Connections established between the spectra of semigroups and their generators

Abstract

We continue to study $\alpha$-times integrated semigroups. Essentially, we characterize the different spectrums of $\alpha$-times integrated semigroups by the spectrums of their generators. Particulary quasi-Fredholm, Kato, essentially Kato, Saphar and essentially Saphar spectrums.