Mathematische Annalen

, Volume 347, Issue 2, pp 455–478 | Cite as

Optimal polynomial decay of functions and operator semigroups

  • Alexander Borichev
  • Yuri TomilovEmail author


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).

Mathematics Subject Classification (2000)

Primary 47D06 Secondary 34D05 46B20 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Centre de Mathématiques et InformatiqueUniversité d’Aix-Marseille IMarseilleFrance
  2. 2.Faculty of Mathematics and Computer ScienceNicolas Copernicus UniversityToruńPoland
  3. 3.Institute of MathematicsPolish Academy of SciencesWarsawPoland

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