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標題: Perturbation of non-exponentially-bounded alpha-times integrated C-semigroups
作者: Li, Y.C.
Shaw, S.Y.
關鍵字: (C-0)-group;alpha-times integrated C-semigroup;subgenerator;generator;perturbation theorem;abstract cauchy-problem;laplace transforms;cosine functions;hille-yosida
Project: Journal of the Mathematical Society of Japan
期刊/報告no:: Journal of the Mathematical Society of Japan, Volume 55, Issue 4, Page(s) 1115-1136.
Let T(.) be a (not necessarily exponentially bounded, not necessarily nondegenerate) alpha-times integrated C-semigroup and let -B be the generator of a (C-0)-group S(.) commuting with T(.) and C. Under suitable conditions on T(.) and S(.) we prove the existence of an alpha-times integrated C-semigroup V(.), which has generator (A+B) over bar 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.
ISSN: 0025-5645
DOI: 10.2969/jmsj/1191418767
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