### 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 iΔ generates a C_{0}-semigroup on L^{P}(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.

Original language | English |
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Pages (from-to) | 635-637 |

Number of pages | 3 |

Journal | Proceedings of the American Mathematical Society |

Volume | 125 |

Issue number | 3 |

Publication status | Published - 1997 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Arendt, W., El Mennaoui, O., & Hieber, M. G. (1997). Boundary values of holomorphic semigroups.

*Proceedings of the American Mathematical Society*,*125*(3), 635-637.