Vol. 51, No. 2, 1974

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
Author Index
To Appear
ISSN: 0030-8730
Subalgebras of finite codimension in the algebra of analytic functions on a Riemann surface

Bruce Stephen Lund

Vol. 51 (1974), No. 2, 495–497

Let R be a finite open Riemann surface with boundary Γ. We set R = R Γ and let A(R) denote the algebra of functions which are continuous on R and analytic on R. Suppose A is a uniform algebra contained in A(R). The main result of this paper shows that if A contains a function F which is analytic in a neighborhood of R and which maps R in a n-to-one manner (counting multiplicity) onto {z : |z|1}, then A has finite codimension in A(R).

Mathematical Subject Classification 2000
Primary: 30A98
Secondary: 46J15
Received: 22 February 1973
Revised: 25 June 1973
Published: 1 April 1974
Bruce Stephen Lund