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International Journal of Mathematics and Mathematical Sciences
Volume 23, Issue 8, Pages 547-554
http://dx.doi.org/10.1155/S0161171200000958

Interpolation by multipliers on certain spaces of analytic functions

Department of Mathematics, Shiraz University, Shiraz, Iran

Received 20 March 1998

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let 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 . Furthermore, assume that z 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 and, in particular, the Dirichlet space.