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Proceedings of the American Mathematical Society

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

 

 

$ L$-analytic mappings in the disk algebra


Author: H. E. Warren
Journal: Proc. Amer. Math. Soc. 39 (1973), 110-116
MSC: Primary 46J15; Secondary 30A98
DOI: https://doi.org/10.1090/S0002-9939-1973-0312278-7
MathSciNet review: 0312278
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Abstract: It is shown that two classes of function transformations coincide when the transformations take place within the disk algebra. The first class is that of the $ L$-analytic mappings. These are the ones given locally by power series: $ f \to {\sum {{g_n}(f - {f_0})} ^n}$. The second class is that of locally pointwise mappings. A mapping $ f \to \Phi [f]$ is pointwise if it has the form $ \Phi [f](x) = {\Phi ^\ast }(x,f(x))$. It is a by-product of the disk algebra investigation that if a set $ X$ has certain topological properties, then every locally pointwise mapping in $ C(X)$ is continuous.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0312278-7
Article copyright: © Copyright 1973 American Mathematical Society