Approximating composition operator norms on the Dirichlet space

Let ϕ be any univalent self-map of the unit disk D whose image Ω ≡ ϕ(D) is compactly contained in D. We provide a method for approximating the norm of the composition operator Cϕ on the Dirichlet space to any desired degree of accuracy. The approximation uses a special basis which is orthogonal in both the Bergman space on the disk and the Bergman space on Ω. Published by Elsevier Inc