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Maximum modulus algebras and singularity sets

Published online by Cambridge University Press:  14 November 2011

John Wermer
John Wermer
Affiliation:
Department of Mathematics, Brown University, Providence, Rhode Island, U.S.A.
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Synopsis

A classical theorem of Hartogs gives conditions on the singularity set of an analytic function of several complex variables in order for such a set to be an analytic variety. A result of E. Bishop from 1963 gives an analogous condition of the maximal ideal space of a uniform algebra in order for this space to have analytic structure. We show that algebras of functions satisfying a maximum principle serve to explain both of these results.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 86 , Issue 3-4 , 1980 , pp. 327 - 331
Copyright
Copyright © Royal Society of Edinburgh 1980

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