A perturbation theorem for operator semigroups in Hilbert spaces

Abstract

We prove a perturbation result for C ₀-semigroups on Hilbert spaces and use it to show that certain operators of the form Au = iu ^(2k) + V · u ^(l) on L ² (ℝ) generate a semigroup that is strongly continuous on (0, ∞).

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Authors and Affiliations

1. Mathematisches Institut I, Universität Karlsruhe (TH), Englerstraße 2, 76128, Karlsruhe, Germany

   C. Kaiser & L. Weis

Authors

1. C. Kaiser
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2. L. Weis
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Correspondence to C. Kaiser.

Additional information

Communicated by Rainer Nagel

The research is supported in part by the Landesforschungsschwerpunkt Evolutionsgleichungen des Landes Baden-Württenberg.

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Kaiser, C., Weis, L. A perturbation theorem for operator semigroups in Hilbert spaces. Semigroup Forum 67, 63–75 (2003). https://doi.org/10.1007/s002330010166

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• Received: 11 March 2002

• Accepted: 22 July 2002

• Published: 28 February 2003

• Issue Date: June 2003

• DOI: https://doi.org/10.1007/s002330010166

Keywords

• Hilbert Space
• Banach Space
• Analytic Semigroup
• Abstract Cauchy Problem
• Semigroup Property