Journal of the European Mathematical Society

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

Fine scales of decay of operator semigroups

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

(1) St John's College, University of Oxford, St Giles, OX1 3JP, Oxford, UK
(2) Institut für Analysis, Technische Universität Dresden, 01062, Dresden, Germany
(3) Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100, Torun, 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