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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Hausdorff content and rational approximation in fractional Lipschitz norms
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by Anthony G. O’Farrell PDF
Trans. Amer. Math. Soc. 228 (1977), 187-206 Request permission

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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Additional Information
  • © Copyright 1977 American Mathematical Society
  • 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