Vol. 51, No. 2, 1974

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 329: 1
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
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