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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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

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