Titlebook: Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics; Wolfgang Arendt,Ralph Chill,Yuri Tomilov Conference

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,Generation of Subordinated Holomorphic Semigroups via Yosida’s Theorem,. is the generator of a holomorphic C.-semigroup on a Banach space, bounded on .. Such estimates are of value, in particular, in approximation theory of operator semigroups. As a corollary, weobtain a new proof of the fact that . generates a holomorphic semigroup whenever −. does, established recent

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Dichotomy Results for Norm Estimates in Operator Semigroups,The results in this survey indicate that the quantitative behaviour of the semigroup at the origin provides additional qualitative information, such as uniform continuity or analyticity.

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Convergence of the Dirichlet-to-Neumann Operator on Varying Domains,We prove resolvent convergence for the Dirichlet-to-Neumann operator on domains which are uniformly starshaped with respect to a ball, when the domains converge appropriately.

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A Banach Algebra Approach to the Weak Spectral Mapping Theorem for Locally Compact Abelian Groups,We give a general version of the weak spectral mapping theorem for non-quasianalytic representations of locally compact abelian groups which are weakly continuous in the sense of Arveson, based on a Banach algebra approach.

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Regularity Properties of Sectorial Operators: Counterexamples and Open Problems,We give a survey on the different regularity properties of sectorial operators on Banach spaces. We present the main results and open questions in the theory and then concentrate on the known methods to construct various counterexamples.

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