Moebius transformations and Blaschke products: the geometric connection.

Authors

Pamela GorkinFollow
Ulrich Daepp, Bucknell UniversityFollow
Andrew ShafferFollow
Karl Voss, Bucknell UniversityFollow

Publication Date

2017

Description

Let B be a degree-n Blaschke product and, for a complex number l of modulus 1, let z_1l, ... z_nl ordered according to increasing argument, denote the (distinct) solutions to B(z) - l = 0. Then there is a smooth curve C such that for each l the line segments joining z_jl and z_(j+1)l are tangent to C. We study the situation in which C is an ellipse and describe the relation to the action of the points z_jl under elliptic disk automorphisms. These results provide a condition for the numerical range of a compressed shift operator with finite Blaschke symbol to be an elliptical disk. We also consider infinite Blaschke products and the action of parabolic and hyperbolic disk automorphisms

Journal

Linear Algebra Appl.

Volume

516

First Page

186

Last Page

211

Department

Mathematics

Link to Published Version

https://doi.org/10.1016/j.laa.2016.11.032

Recommended Citation

Gorkin, Pamela; Daepp, Ulrich; Shaffer, Andrew; and Voss, Karl. "Moebius transformations and Blaschke products: the geometric connection.." Linear Algebra Appl. (2017) : 186-211.