Existence and nonexistence of hypercyclic semigroups

Existence and Nonexistence of Hypercyclic Semigroups

In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any separable infinitedimensional Banach space that is very different from—and considerably shorter than—the one recently given by Bermúdez, Bonilla and Martinón. We also show the existence of a strongly dense family of topologically mixing operators on every separable infinite...

Tensor products of recurrent hypercyclic semigroups

We study tensor products of strongly continuous semigroups on Banach spaces that satisfy the hypercyclicity criterion, the recurrent hypercyclicity criterion or are chaotic.

Existence and Nonexistence of Solutionsfor

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...

Harmonic Homeomorphisms: Existence and Nonexistence

These notes were prepared for International Workshop on Harmonic and Quasiconformal Mappings in Chennai, August 2010. They are based on several papers written jointly with Tadeusz Iwaniec, Jani Onninen, and Ngin-Tee Koh. The source papers are available from www.arxiv.org