Boundary values of holomorphic semigroups

Wolfgang Arendt; Omar El Mennaoui; Matthias Georg Hieber

Boundary values of holomorphic semigroups

Wolfgang Arendt^*, Omar El Mennaoui, Matthias Georg Hieber

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

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 C₀-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

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Cite this

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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 H{\"o}rmander, 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 Pr{\"u}ss one obtains by this theory also a new proof of the classical characterization theorem of holomorphic semigroups.",

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AU - Arendt, Wolfgang

AU - El Mennaoui, Omar

AU - Hieber, Matthias Georg

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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.

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Boundary values of holomorphic semigroups

Abstract

ASJC Scopus subject areas

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