Fractional powers of infinitesimal generators of semigroups (Q2773687)

The author presents a systematic treatment to fractional powers of infinitesimal generators which are based on the Laplace transform. Some basic facts about the operational calculus due to Schwartz are given and the powers of an infinitesimal generator are defined. Certain basic properties of fractional powers such as monotonicity law and power rules are discussed. The results on abstract Riesz potentials given in this article extend the work of Bochner and Riesz on fractional powers of the Laplace transform as well as fractional potentials of negative order. Finally some directions for extensions to more general classes of operators than infinitesimal generators are outlined.NEWLINENEWLINEFor the entire collection see [Zbl 0998.26002].