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Generation of linear evolution operators

Author(s): Naoki Tanaka
Journal: Proc. Amer. Math. Soc. 128 (2000), 2007-2015.
MSC (1991): Primary 47D06; Secondary 34G10
Posted: November 24, 1999
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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.

References:

1.: T. Kato, Linear evolution equations of ``hyperbolic" type, J. Fac. Sci. Univ. Tokyo 17 (1970), 241-258. MR 43:5347
2.: T. Kato, Abstract evolution equations, linear and quasilinear, revisited, Lecture Notes in Math. 1540 (1993), 103-125. MR 95m:34108
3.: K. Kobayasi, On a theorem for linear evolution equations of hyperbolic type, J. Math. Soc. Japan 31 (1979), 647-654. MR 81a:34051
4.: K. Kobayasi and N. Sanekata, A method of iterations for quasi-linear evolution equations in nonreflexive Banach spaces, Hiroshima Math J. 19 (1989), 521-540. MR 91a:34048

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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: 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
Posted: November 24, 1999
Communicated by: Dale Alspach
Copyright of article: Copyright 2000, American Mathematical Society


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