A note on real orthogonal measures

Patrick Robert Ahern and N. V. Rao

Vol. 97 (1981), No. 2, 249–266

DOI: 10.2140/pjm.1981.97.249

Abstract

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

Milestones

Received: 16 April 1979

Published: 1 December 1981