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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Boundary values of holomorphic semigroups
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by Wolfgang Arendt, Omar El Mennaoui and Matthias Hieber PDF
Proc. Amer. Math. Soc. 125 (1997), 635-647 Request permission


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
  • MR Author ID: 26945
  • 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
  • MR Author ID: 270487
  • 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
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 635-647
  • MSC (1991): Primary 47D06, 47F05
  • DOI:
  • MathSciNet review: 1346961