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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Analytic equivalence among simply connected domains in $ C(X)$


Author: Hugh E. Warren
Journal: Trans. Amer. Math. Soc. 196 (1974), 265-288
MSC: Primary 46G20; Secondary 30A98, 46J10
DOI: https://doi.org/10.1090/S0002-9947-1974-0358349-6
MathSciNet review: 0358349
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Abstract: This work considers analytic equivalence within the analytic function theory for commutative Banach algebras which was introduced by E. R. Lorch. Necessary conditions of a geometric nature are given for simply connected domains in $ C(X)$. These show that there are a great many equivalence classes. In some important cases, as when one domain is the unit ball, the given conditions are also sufficient. The main technique is the association of a simply connected domain in $ C(X)$ with a family of Riemann surfaces over the plane.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0358349-6
Keywords: Lorch analytic function, analytic equivalence, Riemann surface
Article copyright: © Copyright 1974 American Mathematical Society

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