In this note we present some constructions with generators of analytic semigroups which are an abstract version of the familiar method of “freezing the coefficients” to prove elliptic estimates for differential operators with continuous coefficients or Hölder-continuous coefficients. As a side result we obtain an abstract exponential decay result for, say eigenfunctions corresponding to isolate...

Abstract: Let X be a Banach space. We define the concept of a bi-parameter semigroup on X and its first and second generators. We also study bi-parameter semigroups on Banach algebras. A relation between uniformly continuous bi-parameter semigroups and σ-derivations is also established. It is proved that if {αt,s}t,s 0 is a uniformly continuous bi-parameter semigroup on a Banach algebra X , who...

Fast control cost for heat-like semigroups: Lebeau-Robbiano strategy and Hautus test Luc Miller (joint work with Thomas Duykaerts) Since the seminal work of Russell and Weiss in [7], resolvent conditions for various notions of admissibility, observability and controllability, and for various notions of linear evolution equations have been studied intensively, sometimes under the name of infinit...

Fast control cost for heat-like semigroups: Lebeau-Robbiano strategy and Hautus test Luc Miller (joint work with Thomas Duykaerts) Since the seminal work of Russell and Weiss in [7], resolvent conditions for various notions of admissibility, observability and controllability, and for various notions of linear evolution equations have been studied intensively, sometimes under the name of infinit...

Abstract The study of analytic semiflows on the open unit disc and the particular form of its infinitesimal generator G makes possible the study of semigroups of composition operators (T (t))t≥0 on various well-known spaces of holomorphic functions such as Hardy, Dirichlet and Bergman spaces. We will provide compactness, analyticity and invertibility complete characterization of (T (t))t≥0 in t...