Vol. 46, No. 2, 1973

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Boundedly holomorphic convex domains

Dong S. Kim

Vol. 46 (1973), No. 2, 441–449
Abstract

A boundedly holomorphic convex domain is a holomorphically convex domain with respect to the algebra of bounded holomorphic functions in the domain. The followings are shown in this paper: In a Riemann domain, a boundedly holomorphic convex domain is a domain of bounded holomorphy. With some restrictions, the converse is true. The spectrum of the algebra B of bounded holomorphic functions is an envelope of bounded holomorphy provided that the completion of B with the topology of uniform convergence on compact subsets is stable under differentiation. Finally, Stein manifolds of bounded type are introduced.

Mathematical Subject Classification 2000
Primary: 32D15
Milestones
Received: 14 December 1971
Revised: 7 July 1972
Published: 1 June 1973
Authors
Dong S. Kim