Holomorphic semigroups and Sarason’s characterization of vanishing mean oscillation

Vanishing Mean Oscillation and Regularity in the Calculus of Variations

compactifications and representations of transformation semigroups

this thesis deals essentially (but not from all aspects) with the extension of the notion of semigroup compactification and the construction of a general theory of semitopological nonaffine (affine) transformation semigroup compactifications. it determines those compactification which are universal with respect to some algebric or topological properties. as an application of the theory, it is i...

Commuting semigroups of holomorphic mappings

Let S1 = {Ft}t≥0 and S2 = {Gt}t≥0 be two continuous semigroups of holomorphic self-mappings of the unit disk ∆ = {z : |z| < 1} generated by f and g, respectively. We present conditions on the behavior of f (or g) in a neighborhood of a fixed point of S1 (or S2), under which the commutativity of two elements, say, F1 and G1 of the semigroups implies that the semigroups commute, i.e., Ft◦Gs = Gs◦...

Metric Domains, Holomorphic Mappings and Nonlinear Semigroups

We study nonlinear semigroups of holomorphic mappings on certain domains in complex Banach spaces. We examine, in particular, their differentiability and their representations by exponential and other product formulas. In addition, we also construct holomorphic retractions onto the stationary point sets of such semigroups.

Semigroups of Holomorphic Functions in the Polydisk

In this paper we provide an easy-to-use characterization of infinitesimal generators of semigroups of holomorphic functions in the polydisk. We also present a number of examples related to that characterization.