|
|||||
|
|
|
|
|
|
|
|
|
A note on fractional
derivatives of semigroups and cosine functions
Hector O. Fattorini |
|
Vol. 109 (1983), No. 2, 335–347
|
Abstract |
|
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 such that t → S(t)u possesses a fractional derivative of order α ≥ 0 coincides with the domain of the α-th 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 Hilbert spaces; in general Banach spaces only an inclusion can be assured. |
Mathematical Subject Classification
Primary: 47D05, 47D05
|
Milestones
Received: 8 May 1981
Revised: 28 May 1982
Published: 1 December 1983
|
Authors |
| Hector O. Fattorini | |
|
