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Proceedings of the American Mathematical Society

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An extension of Runge's theorem


Author: L. A. Rubel
Journal: Proc. Amer. Math. Soc. 47 (1975), 261-262
MSC: Primary 30A82
DOI: https://doi.org/10.1090/S0002-9939-1975-0357806-2
MathSciNet review: 0357806
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Abstract: Every uniformly continuously differentiable function on the compact set $ X$ in the complex plane is the uniform limit of rational functions with poles off $ X$.


References [Enhancements On Off] (What's this?)

  • [B] Andrew Browder, Introduction to function algebras, Benjamin, New York, 1969. MR 39 #7431. MR 0246125 (39:7431)
  • [W] Hassler Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc. 36 (1934), 63-89. MR 1501735

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DOI: https://doi.org/10.1090/S0002-9939-1975-0357806-2
Article copyright: © Copyright 1975 American Mathematical Society

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