Quasi-fredholm and saphar spectrums for the α-times integrated semigroups

Abstract

We continue to study α-times integrated semigroups. Essentially, we characterize the different spectrums of α-times integrated semigroups by the spectrums of their generators. Particulary quasi-Fredholm, Kato, essentially Kato, Saphar and essentially Saphar spectrums.2010 Mathematics Subject Classification. 47D62, 47A10. Key words and phrases. α-times integrated semigroup, quasi-Fredholm, Kato, Saphar, essentially Kato and Saphar.