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October, 2003 Perturbation of non-exponentially-bounded a-times integrated C-semigroups
Yuan-Chuan LI, Sen-Yen SHAW
J. Math. Soc. Japan 55(4): 1115-1136 (October, 2003). DOI: 10.2969/jmsj/1191418767


Let T(·) be a (not necessarily exponentially bounded, not necessarily nondegenerate)α-times integrated C-semigroup and let -B be the generator of a (C0)- group S(·) commuting with T(·) and C. Under suitable conditions on T(·) and S(·) we prove the existence of an α-times integrated C-semigroup V(·), which has generator A+B¯ provided that T(·) is nondegenerate and has generator A. Explicit expressions of V(·) in terms of T(·) and S(·) are obtained. In particular, when B is bounded, V(·) can be constructed by means of a series in terms of T(·) and powers of B.


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Yuan-Chuan LI. Sen-Yen SHAW. "Perturbation of non-exponentially-bounded a-times integrated C-semigroups." J. Math. Soc. Japan 55 (4) 1115 - 1136, October, 2003.


Published: October, 2003
First available in Project Euclid: 3 October 2007

zbMATH: 1067.47057
MathSciNet: MR2003763
Digital Object Identifier: 10.2969/jmsj/1191418767

Primary: 47A55 , 47D60 , 47D62

Keywords: $(C_{0})$-group , generator , perturbation theorem , subgenerator , α-times integrated C-semigroup

Rights: Copyright © 2003 Mathematical Society of Japan


Vol.55 • No. 4 • October, 2003
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