Fine scales of decay of operator semigroups

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.

Version 2 includes numerous minor corrections, and is the authors' final version. The pape will be published in the Journal of the European Mathematical Society in April 2016

References in corpus (2)

• Decay rates for the damped wave equation on the torus
• Polynomial stabilization of some dissipative hyperbolic systems

Cited by in corpus (2)

• Product formulas in functional calculi for sectorial operators
• Robustness of strong stability of semigroups