Vol. 51, No. 2, 1974

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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