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Transactions of the American Mathematical Society

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

 

 

Hausdorff content and rational approximation in fractional Lipschitz norms


Author: Anthony G. O’Farrell
Journal: Trans. Amer. Math. Soc. 228 (1977), 187-206
MSC: Primary 30A82
DOI: https://doi.org/10.1090/S0002-9947-1977-0432887-2
MathSciNet review: 0432887
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Abstract: For $ 0 < \alpha < 1$, we characterise those compact sets X in the plane with the property that each function in the class $ {\text{lip}}(\alpha ,X)$ that is analytic at all interior points of X is the limit in $ {\text{Lip}}(\alpha ,X)$ norm of a sequence of rational functions. The characterisation is in terms of Hausdorff content.


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DOI: https://doi.org/10.1090/S0002-9947-1977-0432887-2
Keywords: Capacity, complex plane
Article copyright: © Copyright 1977 American Mathematical Society