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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Boundary values of holomorphic semigroups


Authors: Wolfgang Arendt, Omar El Mennaoui and Matthias Hieber
Journal: Proc. Amer. Math. Soc. 125 (1997), 635-647
MSC (1991): Primary 47D06, 47F05
MathSciNet review: 1346961
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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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Additional Information

Wolfgang Arendt
Affiliation: Mathematik V, Universität Ulm, D-89069 Ulm, Germany

Omar El Mennaoui
Affiliation: Equipe de Mathématiques, Faculté des Sciences, Université Ibnon Zohr, Agadir, Morocco

Matthias Hieber
Affiliation: Mathematisches Institut I, Universität Karlsruhe, Englerstraße 2, D-76128 Karlsruhe, Germany

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03529-6
PII: S 0002-9939(97)03529-6
Received by editor(s): April 27, 1995
Received by editor(s) in revised form: July 7, 1995
Dedicated: Dedicated to Professor H. H. Schaefer on the Occasion of his 70th Birthday
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society