Existence and nonexistence of universal graphs

Existence and Nonexistence of Solutionsfor

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

Existence and Nonexistence of Descriptive Patterns

In the present paper, we study the existence of descriptive patterns, i. e. patterns that cover all words in a given set through morphisms and that are optimal in terms of revealing commonalities of these words. Our main result shows that if patterns may be mapped onto words by arbitrary morphisms, then there exist infinite sets of words that do not have a descriptive pattern. This answers a qu...

Existence and nonexistence of G � least energy

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...