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Best uniform approximation by harmonic functions on subsets of Riemannian manifolds

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Abstract

We investigate best uniform approximations to bounded, continuous functions by harmonic functions on precompact subsets of Riemannian manifolds. Applications to approximation on unbounded subsets ofR 2 are given.

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Authors and Affiliations

  1. Département de Mathématiques et de Statistique, Université de Montréal, Case postale 6128 Succursale “A”, H3C 3J7, Montréal, Quebec, Canada

    P. M. Gauthier

  2. Department of Mathematics and Statistics, University of Vermont, 16 Colchester Avenue, 05401-1455, Burlington, Vermont, USA

    D. Zwick

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  1. P. M. Gauthier
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  2. D. Zwick
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Communicated by J. Milne Anderson.

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Gauthier, P.M., Zwick, D. Best uniform approximation by harmonic functions on subsets of Riemannian manifolds. Constr. Approx 10, 77–85 (1994). https://doi.org/10.1007/BF01205167

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  • DOI: https://doi.org/10.1007/BF01205167

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