Vol. 97, No. 2, 1981

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A note on real orthogonal measures

Patrick Robert Ahern and N. V. Rao

Vol. 97 (1981), No. 2, 249–266

Let X be an open Riemann surface and K a compact subset of X such that X K has only finitely many connected components. Let R(K) denote the space of meromorphic functions with poles off K. In this note, we investigate the space of real measures supported on ∂K and orthogonal to R(K) and connect it with the first homology group of the interior of K.

Mathematical Subject Classification 2000
Primary: 46J10
Secondary: 30F99
Received: 16 April 1979
Published: 1 December 1981
Patrick Robert Ahern
Department of Mathematics
University of Wisconsin
Madison WI
United States
N. V. Rao