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

 

Spectral conditions guaranteeing a nontrivial
solution of the abstract Cauchy problem


Authors: R. deLaubenfels and S. Wang
Journal: Proc. Amer. Math. Soc. 126 (1998), 3271-3278
MSC (1991): Primary 47D03, 34G10, 47D06, 47A60
MathSciNet review: 1469403
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Abstract | References | Similar Articles | Additional Information

Abstract: We characterize subsets, $\Omega $, of the complex plane, with the following property: If $A$ has spectrum contained in $\Omega $, with polynomially bounded resolvent outside $\Omega $, then the abstract Cauchy problem corresponding to $A$ has a nontrivial solution.


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Additional Information

R. deLaubenfels
Affiliation: Scientia Research Institute, P. O. Box 988, Athens, Ohio 45701
Email: 72260.2403@compuserve.com

S. Wang
Affiliation: Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210008, People’s Republic of China
Email: wang2598@netra.nju.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04572-9
PII: S 0002-9939(98)04572-9
Received by editor(s): June 12, 1996
Received by editor(s) in revised form: March 20, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society