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T-invariant algebras on Riemann surfaces

Part of: Riemann surfaces

Published online by Cambridge University Press:  26 February 2010

André Boivin
André Boivin
Affiliation:
Department of Mathematics, The University of Western Ontario, London, Ontario, Canada, N6A 5B7.
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Abstract

The main purpose of this article is to outline for non-compact Riemann surfaces the development of a theory of T-invariant algebras similar to that developed by T. W. Gamelin [7] in the case of the plane. The main idea is to introduce, using the global local uniformizer of R. C. Gunning and R. Narashimhan, a Cauchy transform operator for the Riemann surface which operates on measures and solves an inhomogeneous -equation. This, in turn, can be used, analogously to the Cauchy transform on the plane, to develop meromorphic (rational) approximation theory. We sketch the path of the development but omit most of the details when they are very much similar to the planar case. Our presentation follows closely that of [7]. The original motivation for this study was to obtain more information on Gleason parts useful in the study of Carleman (tangential) approximation theory (see [5]).

MSC classification

Secondary: 30F99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 34 , Issue 2 , December 1987 , pp. 160 - 171
Copyright
Copyright © University College London 1987

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