645 research outputs found
Optimal polynomial decay of functions and operator semigroups
We characterize the polynomial decay of orbits of Hilbert space
-semigroups in resolvent terms. We also show that results of the same type
for general Banach space semigroups and functions obtained recently in the
paper by C.J.K.Batty and T.Duyckaerts, Non-uniform stability for bounded
semi-groups on Banach spaces (J. Evol. Eq. 2008), are sharp. This settles a
conjecture posed in the paper by C.J.K.Batty and T.Duyckaerts.Comment: 21 pages, to appear in Matematische Annale
Generation of subordinated holomorphic semigroups via Yosida's theorem
Using functional calculi theory, we obtain several estimates for
, where is a Bernstein function, is a bounded
completely monotone function and is the generator of a holomorphic
-semigroup on a Banach space, bounded on . Such estimates are
of value, in particular, in approximation theory of operator semigroups. As a
corollary, we obtain a new proof of the fact that generates a
holomorphic semigroup whenever does, established recently in [8] by a
different approach
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