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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A generalized Shilov boundary and analytic structure


Author: Richard F. Basener
Journal: Proc. Amer. Math. Soc. 47 (1975), 98-104
MathSciNet review: 0352990
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Abstract: A generalization of the concept of the Shilov boundary of a uniform algebra is introduced. This makes it possible to formulate and prove several-dimensional analogues of certain well-known results which guarantee the existence of one-dimensional analytic structure when a function in the algebra is finite-to-one over a suitable part of its spectrum.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0352990-9
Keywords: Analyticity, maximal ideal space, Shilov boundary
Article copyright: © Copyright 1975 American Mathematical Society