Asymptotic behaviour of semigroups of operators
نویسندگان
چکیده
منابع مشابه
On the Asymptotic Behaviour of Perturbed Semigroups
We give conditions on a strongly continuous semigroup T and a bounded perturbation B such that the perturbed semigroup S preserves asymptotic properties as boundedness, asymptotic almost periodicity, uniform ergodicity and total uniform ergodicity. In the rst systematic treatise on perturbation of semigroups, R.S.Phillips 10] proved in 1953 that, if A is the innnitesimal generator of a strongly...
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and Applied Analysis 3 then lim k Uf Lf, ∀f ∈ C X . 3.2 Moreover, if X is a compact metric space, then the convergence is uniform. Proof. Let f ∈ C X . The case when Lf f is trivial. Indeed, in this case, since Lf ∈ V andU preserves the elements of V, we haveUf ULf Lf , and hence Uf Lf , k 1, 2, . . . . If Lf / f , for sufficiently small ε > 0, the inverse image of the open set −ε, ε under the ...
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ژورنال
عنوان ژورنال: Banach Center Publications
سال: 1994
ISSN: 0137-6934,1730-6299
DOI: 10.4064/-30-1-35-52