×

zbMATH — the first resource for mathematics

Laplace transforms and \(\alpha\)-times integrated semigroups. (English) Zbl 0766.47013
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.

MSC:
47D06 One-parameter semigroups and linear evolution equations
34G10 Linear differential equations in abstract spaces
PDF BibTeX XML Cite
Full Text: DOI EuDML