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

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- by Hugh E. Warren
- Trans. Amer. Math. Soc.
**196**(1974), 265-288 - DOI: https://doi.org/10.1090/S0002-9947-1974-0358349-6
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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.## References

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## Bibliographic Information

- © Copyright 1974 American Mathematical Society
- 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