Abstract
We characterize the polynomial decay of orbits of Hilbert space C 0-semigroups in resolvent terms. We also show that results of the same type for general Banach space semigroups and functions obtained recently in Batty and Duyckaerts (J Evol Eq 8:765–780, 2008) are sharp. This settles a conjecture posed in Batty and Duyckaerts (2008).
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The authors were partially supported by the Marie Curie “Transfer of Knowledge” programme, project “TODEQ”. The first author was also partially supported by the ANR project DYNOP. The second author was also partially supported by a MNiSzW grant Nr. N201384834.
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Borichev, A., Tomilov, Y. Optimal polynomial decay of functions and operator semigroups. Math. Ann. 347, 455–478 (2010). https://doi.org/10.1007/s00208-009-0439-0
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DOI: https://doi.org/10.1007/s00208-009-0439-0