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Transactions of the American Mathematical Society

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

 

 

Analytic equivalence in the disk algebra


Author: Hugh E. Warren
Journal: Trans. Amer. Math. Soc. 192 (1974), 219-226
MSC: Primary 46J99
DOI: https://doi.org/10.1090/S0002-9947-1974-0333742-6
MathSciNet review: 0333742
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Abstract: The notion of analytically equivalent domains can be extended from the complex plane to commutative Banach algebras with identity. In $ C(X)$ a domain equivalent to the unit ball must have a boundary that is in a certain sense continuous. This paper shows that in the disk algebra ``continuous'' must be replaced with ``analytic.'' These results set limits in the classical Riemann mapping theorem on how smoothly the mapping can respond to changes in the domain being mapped.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0333742-6
Keywords: Disk algebra, Lorch analytic function, analytic equivalence
Article copyright: © Copyright 1974 American Mathematical Society