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Proceedings of the American Mathematical Society

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

 

 

On approximation by rationals from a hyperplane


Authors: Gerhard Gierz and Boris Shekhtman
Journal: Proc. Amer. Math. Soc. 96 (1986), 452-454
MSC: Primary 41A20
MathSciNet review: 822438
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Abstract: Let $ E \subset C(K)$ be a subspace of continuous functions defined on a compact Hausdorff space $ K$. We characterize those subspaces of codimension 1 for which the rational functions with denominators and enumerators from $ E$ are dense. The condition for the density of this very nonlinear set of functions turns out to be a linear separation condition.


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

  • [1] Donald J. Newman, Approximation with rational functions, CBMS Regional Conference Series in Mathematics, vol. 41, Conference Board of the Mathematical Sciences, Washington, D.C., 1979. Expository lectures from the CBMS Regional Conference held at the University of Rhode Island, Providence, R.I., June 12–16, 1978. MR 539314
  • [2] Helmut H. Schaefer, Banach lattices and positive operators, Springer-Verlag, New York-Heidelberg, 1974. Die Grundlehren der mathematischen Wissenschaften, Band 215. MR 0423039

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DOI: https://doi.org/10.1090/S0002-9939-1986-0822438-3
Article copyright: © Copyright 1986 American Mathematical Society