\(\alpha\)-times integrated semigroups \((\alpha\in \mathbb{R}^ +)\)
\(\alpha\)-times integrated semigroups for any \(\alpha>0\) were introduced by \textit{M. Hieber} [Forum Math. 3, 595-612 (1991; Zbl 0766.47013)] where, among other things, a Hille-Yosida type theorem was proved. Further study was done by \textit{M. Hieber} [Math. Ann. 291, No. 1, 1-16 (1991; Zbl 0737.34043)], and \textit{I. Miyadera}, \textit{M. Okubo} and \textit{N. Tanaka} [Mem. Sch. Sci. Eng., Waseda Univ. 57, 267-289 (1993; Zbl 0814.47049)]. The present article presents some results similar to those of Hieber, whose papers apparently were not available to the authors at this time.
scientific article; zbMATH DE number 1046962