To the theory of infinitely differentiable semigroups of operators. (English. Russian original) Zbl 1244.47018
St. Petersbg. Math. J. 22, No. 2, 175-182 (2011); translation from Algebra Anal. 22, No. 2, 1-13 (2010).
The author constructs an infinitely differentiable semigroup of linear bounded operators from a given multivalued linear operator with certain growth restrictions on the resolvent. It is shown that the multivalued linear operator is a generator of this semigroup. The results are usable in the study of linear differential inclusions of the form
\[
\dot{x}(t)\in \mathcal{A}\,x(t),\qquad t\geq 0,
\]
where \(\mathcal{A}\) ia a multivalued linear operator. This work develop the corresponding results in the monograph [E. Hille and R. S. Phillips, Functional analysis and semigroups. Colloquium Publications 31. Providence: R. I. American Mathematical Society (AMS) (1957; Zbl 0078.10004)].
Reviewer: Yongxiang Li (Lanzhou)
MSC:
| 47A56 | Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) |
| 47D06 | One-parameter semigroups and linear evolution equations |
| 34A60 | Ordinary differential inclusions |
Keywords:
linear relation; infinitely differentiable semigroup of operators; generator of a semigroup; resolvent setCitations:
Zbl 0078.10004References:
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