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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Generation of linear evolution operators


Author: Naoki Tanaka
Journal: Proc. Amer. Math. Soc. 128 (2000), 2007-2015
MSC (1991): Primary 47D06; Secondary 34G10
Published electronically: November 24, 1999
MathSciNet review: 1654080
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Abstract: This paper is devoted to the problem of generation of evolution operators associated with linear evolution equations in a general Banach space. The stability condition is proposed from the viewpoint of finite difference approximations. It is shown that linear evolution operators can be generated even if the stability condition given here is assumed instead of Kato's stability condition.


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Additional Information

Naoki Tanaka
Affiliation: Department of Mathematics, Faculty of Science, Okayama University, Okayama 700-8530, Japan
Email: tanaka@math.okayama-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05263-6
PII: S 0002-9939(99)05263-6
Keywords: Linear evolution operator, stability condition, intertwining condition
Received by editor(s): May 4, 1998
Received by editor(s) in revised form: August 24, 1998
Published electronically: November 24, 1999
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society