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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

S. Wang
Affiliation: Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210008, People’s Republic of China

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