Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 55, Number 4 (2003), 1115-1136.
Perturbation of non-exponentially-bounded -times integrated -semigroups
Let be a (not necessarily exponentially bounded, not necessarily nondegenerate)-times integrated -semigroup and let be the generator of a group commuting with and . Under suitable conditions on and we prove the existence of an -times integrated -semigroup , which has generator provided that is nondegenerate and has generator . Explicit expressions of in terms of and are obtained. In particular, when is bounded, can be constructed by means of a series in terms of and powers of .
J. Math. Soc. Japan, Volume 55, Number 4 (2003), 1115-1136.
First available in Project Euclid: 3 October 2007
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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. https://projecteuclid.org/euclid.jmsj/1191418767