Abstract

Let ℋ be a Hilbert space of analytic functions on a planar domain G such that, for each λ in G, the linear functional eλ of evaluation at λ is bounded on ℋ. Furthermore, assume that zℋ⊂ℋ and σ(Mz)=G¯ is an M-spectral set for Mz, the operator of multiplication by z. This paper is devoted to the study of interpolation by multipliers of the space ℋ and, in particular, the Dirichlet space.