Vol. 35, No. 2, 1970

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
An approximation theorem for subalgebras of H∞

Arne Stray

Vol. 35 (1970), No. 2, 511–515
Abstract

Let E be a closed subset of the unitcircle T = {z : |z| = 1} and denote by BE the algebra of all functions which are bounded and continuous on the set X = {z : |z|1&zE} and analytic in D = {z : |z| < 1}.

The main result of this paper (Theorem 1) is that there exist an open set V E containing X such that every f BE can be approximated uniformly on X by functions being analytic in V E.

Mathematical Subject Classification
Primary: 46.55
Milestones
Received: 30 December 1969
Published: 1 November 1970
Authors
Arne Stray
Mathematics Institute
University of Bergen
5007 Bergen
Norway