### 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 |
---|---|

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 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*125*(3), 635-637.

**Boundary values of holomorphic semigroups.** / Arendt, Wolfgang; El Mennaoui, Omar; Hieber, Matthias Georg.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 125, no. 3, pp. 635-637.

}

TY - JOUR

T1 - Boundary values of holomorphic semigroups

AU - Arendt, Wolfgang

AU - El Mennaoui, Omar

AU - Hieber, Matthias Georg

PY - 1997

Y1 - 1997

N2 - 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 C0-semigroup on LP(ℝN) 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.

AB - 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 C0-semigroup on LP(ℝN) 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.

UR - http://www.scopus.com/inward/record.url?scp=21744440523&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21744440523&partnerID=8YFLogxK

M3 - Article

VL - 125

SP - 635

EP - 637

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 3

ER -