-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 -analytic mappings. These are the ones given locally by power series: . The second class is that of locally pointwise mappings. A mapping is pointwise if it has the form . It is a by-product of the disk algebra investigation that if a set has certain topological properties, then every locally pointwise mapping in is continuous.

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DOI:
https://doi.org/10.1090/S0002-9939-1973-0312278-7

Article copyright:
© Copyright 1973
American Mathematical Society