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Optimal polynomial decay of functions and operator semigroups

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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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Authors and Affiliations

  1. Centre de Mathématiques et Informatique, Université d’Aix-Marseille I, 39 rue Frédéric Joliot-Curie, 13453, Marseille, France

    Alexander Borichev

  2. Faculty of Mathematics and Computer Science, Nicolas Copernicus University, ul. Chopina 12/18, 87-100, Toruń, Poland

    Yuri Tomilov

  3. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich str. 8, 00-956, Warsaw, Poland

    Yuri Tomilov

Authors
  1. Alexander Borichev
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  2. Yuri Tomilov
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Correspondence to Yuri Tomilov.

Additional information

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

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