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Spectral conditions guaranteeing a nontrivial solution of the abstract Cauchy problem
Author(s):
R.
deLaubenfels;
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:
We characterize subsets,  , of the complex plane, with the following property: If  has spectrum contained in  , with polynomially bounded resolvent outside  , then the abstract Cauchy problem corresponding to  has a nontrivial solution.
References:
- [1]
- E. B. Davies, ``One-parameter Semigroups,'' London Math. Soc. Monographs 15, Academic Press, 1980. MR 82i:47060
- [2]
- R. deLaubenfels ``Existence Families, Functional Calculi and Evolution Equations,'' Lecture Notes in Mathematics 1570, Springer Verlag, Berlin 1994. MR 96b:47047
- [3]
- R. deLaubenfels, G. Sun and S. Wang, Regularized semigroups, existence families and the abstract Cauchy problem, J. Diff. and Int. Eqns. 8 (1995), 1477-1496. MR 96j:47035
- [4]
- R. deLaubenfels, Automatic extensions of functional calculi, Studia Math. 114 (1995), 237-259. MR 96f:47029
- [5]
- J. A. Goldstein, ``Semigroups of Linear Operators and Applications,'' Oxford, New York, 1985. MR 87c:47056
- [6]
- A. Pazy, ``Semigroups of Linear Operators and Applications to Partial Differential Equations,'' Springer, New York, 1983. MR 85g:47061
- [7]
- J. A. van Casteren, ``Generators of Strongly Continuous Semigroups,'' Research Notes in Mathematics 115, Pitman, Boston, 1985. Zbl. 576:47023
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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:
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
Copyright of article:
Copyright
1998,
American Mathematical Society
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