Semi-Fredholm and semi-Browder spectrums for the ${\alpha}$-times integrated semigroups

TL;DR

This paper investigates the spectral properties of -times integrated semigroups, relating their spectra to those of their generators, with a focus on essential ascent, descent, and semi-Fredholm and semi-Browder spectrums.

Contribution

It introduces a detailed analysis of various spectrums for -times integrated semigroups, extending the understanding of their spectral behavior.

Findings

Characterization of essential ascent and descent for -times integrated semigroups

Descriptions of upper and lower semi-Fredholm spectrums

Descriptions of semi-Browder spectrums for these semigroups

Abstract

In this paper, we describe the different spectrums of the {\alpha}-times integrated semigroups by the spectrums of their generators. Specially, essential ascent and descent, upper and lower semi-Fredholm and semi-Browder spectrums.