Fine scales of decay of operator semigroups

2013/05/23 by Batty, Charles, Chill, Ralph, Tomilov, Yuri · 1 citation
#47D06 34D05 34D10 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1305.5365

Abstract

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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• Relation between semigroup growth and resolvent decay for immediately differentiable semigroups

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