International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 8, Pages 547-554
doi:10.1155/S0161171200000958

Interpolation by multipliers on certain spaces of analytic functions

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.