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Proceedings of the American Mathematical Society

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

 

 

The peak sets of $ A\sp{m}$


Authors: B. A. Taylor and D. L. Williams
Journal: Proc. Amer. Math. Soc. 24 (1970), 604-606
MSC: Primary 30.70
DOI: https://doi.org/10.1090/S0002-9939-1970-0255828-9
MathSciNet review: 0255828
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Abstract: Let $ A$ denote the algebra of functions analytic for $ \vert z\vert < 1$ and continuous for $ \vert z\vert \leqq 1$. For $ m = 1,2, \cdots ,$, let $ {A^m}$ be the algebra of functions $ f$ such that $ f,f', \cdots ,{f^{(m)}} \in A$; and let $ {A^\infty } = \cap _{m = 1}^\infty {A^m}$. We show that the peak sets of $ {A^m},1 \leqq m \leqq \infty $, are the finite subsets of $ \{ \vert z\vert = 1\} $.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0255828-9
Keywords: Algebra of analytic functions, boundary values of analytic functions, peak set, interpolation
Article copyright: © Copyright 1970 American Mathematical Society