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International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 1, Pages 39-46

Banach spaces of functions analytic in a polydisc

Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla 65401, Missouri, USA

Received 8 March 1985

Copyright © 1986 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.


This paper is concerned with functions of several complex variables analytic in the unit polydisc. Certain Banach spaces to which these functions might belong are defined and some relationships between them are developed. The space of linear functionals for the Banach space of functions analytic in the open unit polydisc and continuous on the unit torus is then described in terms of analytic functions using an extension of the Hadamard product.