Vol. 9, No. 5, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 11, 1 issue

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
Cover Page
Editorial Board
Editors’ Addresses
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Subscriptions
Editorial Login
Author Index
Coming Soon
Contacts
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Spectrum of a composition operator with automorphic symbol

Robert F. Allen, Thong M. Le and Matthew A. Pons

Vol. 9 (2016), No. 5, 813–829
Abstract

We give a complete characterization of the spectrum of composition operators, induced by an automorphism of the open unit disk, acting on a family of Banach spaces of analytic functions that includes the Bloch space and BMOA. We show that for parabolic and hyperbolic automorphisms the spectrum is the unit circle. For the case of elliptic automorphisms, the spectrum is either the unit circle or a finite cyclic subgroup of the unit circle.

Keywords
composition operator, spectrum, automorphism
Mathematical Subject Classification 2010
Primary: 47A10, 47B33
Secondary: 30H05
Milestones
Received: 24 June 2015
Revised: 26 August 2015
Accepted: 7 September 2015
Published: 25 August 2016

Communicated by Stephan Garcia
Authors
Robert F. Allen
Department of Mathematics and Statistics
University of Wisconsin-La Crosse
La Crosse, WI 54601
United States
Thong M. Le
Department of Computer Science
University of California, Davis
Davis, CA 95616
United States
Matthew A. Pons
Department of Mathematics
North Central College
Naperville, IL 60540
United States