The norm of a composition operator with linear symbol acting on the Dirichlet space

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.  2004 Elsevier Inc. All rights reserved.