Boundary values of holomorphic semigroups

Abstract

The concept of boundary values of holomorphic semigroups is used to give a new proof of a result due to Hörmander, saying that the operator i Δ i\Delta generates a C 0 C_0 -semigroup on L p ( R N ) L^p(\mathbb R^N) if and only if p = 2 p=2 . Using a recent result on Laplace transforms by Prüss one obtains by this theory also a new proof of the classical characterization theorem of holomorphic semigroups.