Journal of the European Mathematical Society

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Volume 18, Issue 4, 2016, pp. 853–929
DOI: 10.4171/JEMS/605

Published online: 2016-03-08

Fine scales of decay of operator semigroups

Charles J.K. Batty[1], Ralph Chill[2] and Yuri Tomilov[3]

(1) University of Oxford, UK
(2) Technische Universität Dresden, Germany
(3) Nicolaus Copernicus University, Toruń, Poland

Motivated by potential applications to partial differential equations, we develop a theory of fine scales of decay rates for operator semigroups. The theory contains, unifies, and extends several notable results in the literature on decay of operator semigroups and yields a number of new ones. Its core is a new operator-theoretical method of deriving rates of decay combining ingredients from functional calculus and complex, real and harmonic analysis. It also leads to several results of independent interest.

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Batty Charles J.K., Chill Ralph, Tomilov Yuri: Fine scales of decay of operator semigroups. J. Eur. Math. Soc. 18 (2016), 853-929. doi: 10.4171/JEMS/605