The group of invariants of an inner function with finite spectrum

Abstract

This paper determines the group of continuous invariants corresponding to an inner function $\Theta$ with finitely many singularities on the unit circle $T$; that is, the continuous mappings $g:T\to T$ such that $\Theta \circ g=\Theta$ on $\T$. These mappings form a group under composition.

14 pages, 3 figures, submitted for publication May 2010