ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ - ΤΜΗΜΑ ΜΑΘΗΜΑΤΙΚΩΝ
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ΣΕΜΙΝΑΡΙΟ ΑΝΑΛΥΣΗΣ

Γιώργος Κωστάκης
University of Edinburgh

Ιούλιος 2004

Ο Δρ. Γ. Κωστάκης επισκέπτεται το Τμήμα Μαθηματικών για δύο εβδομάδες από 12 Ιουλίου 2004. Θα δώσει δύο ομιλίες (δείτε τη τη σελίδα του Σεμιναρίου Ανάλυσης για το πότε και πού) με τα ακόλουθα θέματα.

  1. On the Growth of Hypercyclic Entire Functions
    Let $D$ be the differentiation operator and $T_1$ the translation operator by $1$, both acting on the space of entire functions. In this talk, we discuss the growth rates of hypercyclic entire functions for the composition operator $D\circ T_1$. We further investigate the growth properties of hypercyclic entire functions for the sequence of operators $\,\left\{ D^n\circ R_{\lambda} \right\}_{n\geq 0}\,$ and $\,\left\{ D^n\circ R_{\lambda}\circ T_1^n \right\}_{n\geq 0}\,$ where $R_{\lambda}$ denotes the dilation operator by $\lambda \in \mathbb{C}\setminus \{ 0\}$.

  2. Common Cesaro Hypercyclic Vectors
    The notion of hypercyclicity is related to the dynamics of linear operators on infinite dimensional topological vector spaces. In this talk we shall present a proof of the existence of common Cesaro hypercyclic vectors for certain classes of operators as multiples of the backward shift and translation operators as well. In order to do so, we first establish a version of Ansari's theorem for operators being hypercyclic and Cesaro hypercyclic.


Mihalis Kolountzakis 2004-07-10