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.
Cite this article
Charles J.K. Batty, Ralph Chill, Yuri Tomilov, Fine scales of decay of operator semigroups. J. Eur. Math. Soc. 18 (2016), no. 4, pp. 853–929DOI 10.4171/JEMS/605