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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
In this paper we investigate commutator conditions for two strongly continuous semigroups and
on a Banach space implying the convergence of the Lie-Trotter products
. 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