Journal of the Mathematical Society of Japan

Perturbation of non-exponentially-bounded a-times integrated C-semigroups

Yuan-Chuan LI and Sen-Yen SHAW

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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.

Article information

J. Math. Soc. Japan, Volume 55, Number 4 (2003), 1115-1136.

First available in Project Euclid: 3 October 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47D60: $C$-semigroups, regularized semigroups 47D62: Integrated semigroups 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15]

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


LI, Yuan-Chuan; SHAW, Sen-Yen. Perturbation of non-exponentially-bounded $a$ -times integrated $C$ -semigroups. J. Math. Soc. Japan 55 (2003), no. 4, 1115--1136. doi:10.2969/jmsj/1191418767.

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