**"****Boundedness of Composition Operators on Hardy Spaces
of the Half-plane via Reproducing Kernels****"**

By

**Abstract:** It is
very well known that every composition operator on Hardy spaces of the unit
disc is bounded whereas the boundedness of
composition operators on Hardy spaces of the half-plane is not always possible.
In 1999 Matache characterized the boundedness
of composition operators of the half-plane in terms of Carleson
measures. In 2012 M. Jury and S. Elliott, using the theory of positive kernels,
found a geometrical criterion in terms of the derivative of the inducing
function at infinity for the boundedness of
composition operators of the half-plane. In this talk we will survey the result
of Jury and Elliott. I will give a brief introduction to the theory of positive
kernels. We will also discuss the posibility of
extending the method of Jury and Elliott to Hardy spaces of the poly-disc.

**Date: ****Tuesday, November 12, 2013**

**Time: ****16.00**

**Place: ****Mathematics Seminar Room,
SA-141**

Tea and cookies will be served before the
seminar.