Hieber, Matthias Laplace transforms and \(\alpha\)-times integrated semigroups. (English) Zbl 0766.47013 Forum Math. 3, No. 6, 595-612 (1991). Summary: We introduce \(\alpha\)-times integrated semigroups for positive real numbers \(\alpha\). A Hille-Yosida type characterization of their generators is given as a consequence of a vector-valued version of Widder’s theorem. Finally the connection between \(\alpha\)-times integrated semigroups and the abstract Cauchy problem is investigated. Cited in 3 ReviewsCited in 33 Documents MSC: 47D06 One-parameter semigroups and linear evolution equations 34G10 Linear differential equations in abstract spaces Keywords:integrated semigroups; Hille-Yosida type characterization of their generators; vector-valued version of Widder’s theorem; abstract Cauchy problem PDFBibTeX XMLCite \textit{M. Hieber}, Forum Math. 3, No. 6, 595--612 (1991; Zbl 0766.47013) Full Text: DOI EuDML