International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 648597, 18 pages
doi:10.1155/2010/648597
Research Article

Normed Domains of Holomorphy

Steven G. Krantz

Department of Mathematics, Washington University in St. Louis, St. Louis, MI 63130, USA

Received 25 October 2009; Accepted 24 December 2009

Academic Editor: Mona amal Aouf

Copyright © 2010 Steven G. Krantz. 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

We treat the classical concept of domain of holomorphy in ℂn when the holomorphic functions considered are restricted to lie in some Banach space. Positive and negative results are presented. A new view of the case n=1 is considered.