Boundary values of holomorphic semigroups

Arendt, Wolfgang; El Mennaoui, Omar; Hieber, Matthias

doi:10.1090/S0002-9939-97-03529-6

Boundary values of holomorphic semigroups
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by Wolfgang Arendt, Omar El Mennaoui and Matthias Hieber

Proc. Amer. Math. Soc. 125 (1997), 635-647

DOI: https://doi.org/10.1090/S0002-9939-97-03529-6

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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 $i\Delta$ generates a $C_0$-semigroup on $L^p(\mathbb R^N)$ if and only if $p=2$. 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.

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