Commutator conditions implying the convergence of the Lie–Trotter products

Kühnemund, Franziska; Wacker, Markus

doi:10.1090/S0002-9939-01-06034-8

Commutator conditions implying the convergence of the Lie-Trotter products

Authors: Franziska Kühnemund and Markus Wacker
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
Published electronically: April 25, 2001
MathSciNet review: 1860489
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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.

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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

DOI: https://doi.org/10.1090/S0002-9939-01-06034-8
Keywords: Strongly continuous semigroups, Trotter--Lie product formula, commutator conditions, Weyl relation, Ornstein--Uhlenbeck semigroup
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
Article copyright: © Copyright 2001 American Mathematical Society