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Recent documents in Mathematics Faculty Publicationsen-usFri, 22 Mar 2013 14:38:18 PDT3600Isolation and component structure in spaces of composition operators
http://digitalcommons.conncoll.edu/mathfacpub/5
http://digitalcommons.conncoll.edu/mathfacpub/5Tue, 05 Feb 2013 11:43:30 PST
We establish a condition that guarantees isolation in the space of composition operators acting between H^{p }(B_{N }) and H^{q }(B_{N }), for 0 < p ≤ ∞, 0 < q < ∞, and N ≥ 1. This result will allow us, in certain cases where 0 < q < p ≤ ∞, completely to characterize the component structure of this space of operators.
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Christopher Hammond et al.The norm of a composition operator with linear symbol acting on the Dirichlet space
http://digitalcommons.conncoll.edu/mathfacpub/4
http://digitalcommons.conncoll.edu/mathfacpub/4Tue, 05 Feb 2013 10:16:33 PST
We obtain a representation for the norm of a composition operator on the Dirichlet space induced by a map of the form φ(z)=az+b. We compare this result to an upper bound for ‖Cφ‖ that is valid whenever φ is univalent. Our work relies heavily on an adjoint formula recently discovered by Gallardo-Gutiérrez and Montes-Rodríguez.
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Christopher HammondAdjoints of composition operators with rational symbol
http://digitalcommons.conncoll.edu/mathfacpub/3
http://digitalcommons.conncoll.edu/mathfacpub/3Tue, 05 Feb 2013 09:30:20 PST
Building on techniques developed by C. C. Cowen and E. A. Gallardo-Gutiérrez [J. Funct. Anal. 238 (2006), no. 2, 447–462;MR2253727 (2007e:47033)], we find a concrete formula for the adjoint of a composition operator with rational symbol acting on the Hardy space H ^{2} . We consider some specific examples, comparing our formula with several results that were previously known.
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Christopher Hammond et al.Norms of linear-fractional composition operators
http://digitalcommons.conncoll.edu/mathfacpub/2
http://digitalcommons.conncoll.edu/mathfacpub/2Tue, 05 Feb 2013 09:05:36 PSTPaul S. Bourdon et al.Composition operators with maximal norm on weighted Bergman spaces
http://digitalcommons.conncoll.edu/mathfacpub/1
http://digitalcommons.conncoll.edu/mathfacpub/1Mon, 04 Feb 2013 12:07:18 PST
We prove that any composition operator with maximal norm on one of the weighted Bergman spaces is induced by a disk automorphism or a map that fixes the origin. This result demonstrates a major difference between the weighted Bergman spaces and the Hardy space H^{2}, where every inner function induces a composition operator with maximal norm.
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Brent J. Carswell et al.