Commutator conditions implying the convergence of the Lie–Trotter products
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- by Franziska Kühnemund and Markus Wacker PDF
- Proc. Amer. Math. Soc. 129 (2001), 3569-3582 Request permission
Abstract:
In this paper we investigate commutator conditions for two strongly continuous semigroups ${(T(t))_{t\geq 0} }$ and ${(S(t))_{t\geq 0} }$ on a Banach space implying the convergence of the Lie–Trotter products $[T(\tfrac {t}{n})S(\tfrac {t}{n})]^n$. The results are then applied to various examples and, in particular, to the Ornstein–Uhlenbeck operator.References
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Additional Information
- Franziska Kühnemund
- Affiliation: Mathematisches Institut, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
- Email: frku@michelangelo.mathematik.uni-tuebingen.de
- Markus Wacker
- Affiliation: Mathematisches Institut, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
- Email: mawa@michelangelo.mathematik.uni-tuebingen.de
- Received by editor(s): December 16, 1999
- Received by editor(s) in revised form: April 14, 2000
- Published electronically: April 25, 2001
- Additional Notes: The authors thank Giorgio Metafune, Rainer Nagel, Abdelaziz Rhandi and Roland Schnaubelt for helpful discussions.
- Communicated by: David R. Larson
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 3569-3582
- MSC (2000): Primary 34G10, 35K15, 47D06
- DOI: https://doi.org/10.1090/S0002-9939-01-06034-8
- MathSciNet review: 1860489