The norm of a composition operator with linear symbol acting on the Dirichlet space |
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Authors: | Christopher Hammond |
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Institution: | Connecticut College, Box 5384, 270 Mohegan Avenue, New London, CT 06320, USA |
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Abstract: | 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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Keywords: | Composition operator Dirichlet space |
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