Optimal polynomial decay of functions and operator semigroups

Alexander Borichev (1) , Yuri Tomilov (2)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 PAN - Institut of Mathematics - Polish Academy of Sciences

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).

Domaines: Analyse fonctionnelle [math.FA]; Equations aux dérivées partielles [math.AP]

Alexander Borichev, Yuri Tomilov. Optimal polynomial decay of functions and operator semigroups. Mathematische Annalen, 2010, 347 (2), ⟨10.1007/s00208-009-0439-0⟩. ⟨hal-01257778⟩