A note on fractional derivatives of semigroups and cosine functions
A note on fractional derivatives of semigroups and cosine functions
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DOI：
10.2140/pjm.1983.109.335
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发表时间：
1983-12
影响因子：
0.6
通讯作者：
H. Fattorini
中科院分区：
文献类型：
--
作者：
H. Fattorini
小松证明，如果 S() 是 Banach 空间 E 中的强连续半群，则所有 u E E 的空间，使得 / —> S(t)u 拥有 a > 0 阶的分数阶导数，与无穷小生成元 A（的平移）的 α 次幂的域一致。我们在这里证明，类似的关系对于强连续余弦函数成立，至少如果 E 属于 a 类包括休伯特空间；在一般巴纳赫空间中，只能保证包含。
It was proved by Komatsu that if S() is a strongly continuous semigroup in a Banach space E then the space of all u E E such that / —> S(t)u possesses a fractional derivative of order a > 0 coincides with the domain of the αth power of (a translate of) the infinitesimal generator A. We prove here that a similar relationship holds for strongly continuous cosine functions, at least if E belongs to a class including Hubert spaces; in general Banach spaces only an inclusion can be assured.