Corrigendum to “On the spectral bound of the generator of a -semigroup” (Studia Math. 125 (1997), 23-33)
Some statements of the paper [4] are corrected.
Domain characterizations of certain functions of power-bounded operators
We create a general framework for describing domains of functions of power-bounded operators given by power series with log-convex coefficients. This sheds new light on recent results of Assani, Derriennic, Lin and others. In particular, we resolve an open problem regarding the "one-sided ergodic Hilbert transform" formulated in a 2001 paper by Derriennic and Lin.
Stability of operator semigroups: ideas and results
Fine scales of decay of operator semigroups
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...
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