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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
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Abstract |
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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 . 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
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Mathematical Subject Classification 2010
Primary: 47A10, 47B33
Secondary: 30H05
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Milestones
Received: 24 June 2015
Revised: 26 August 2015
Accepted: 7 September 2015
Published: 25 August 2016
Communicated by Stephan Garcia
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Authors |
| Robert F. Allen | |
| Department of Mathematics and
Statistics University of Wisconsin-La Crosse La Crosse, WI 54601 United States |
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| Thong M. Le | |
| Department of Computer Science University of California, Davis Davis, CA 95616 United States |
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| Matthew A. Pons | |
| Department of Mathematics North Central College Naperville, IL 60540 United States |
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