# Joline Granath: Finite Blaschke products and their properties

BSc thesis presentation

**Time: **
Tue 2020-06-02 14.30 - 15.30

**Lecturer: **
Joline Granath

**Location: **
Zoom, meeting ID: 654 5097 1372

**Supervisor: **
Annemarie Luger

### Abstract

A finite Blaschke product B(z) is a special kind of product of finitely many automorphisms of the unit disc, with zeros in a finite set of points on the unit disc. This thesis covers some basic properties regarding finite Blaschke products. Solutions to the equation B(z)=w for w inside, on and outside the unit circle are examined, as well as zeros of B(z) and the derivative B'(z), and their location. In the last section, geometrical properties of the solutions to the equation B(z)=w for w on the unit circle are explored; when the Blaschke product is of degree three, this involves ellipses.