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Order of approximation by electrostatic fields due to electrons

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Abstract

LetD be a Jordan domain in the complex plane andA q (D) the Bers space with norm ∥ ∥ q . IfD is the unit disk, it is known that ∥S n 0∥2≥π/18, whereS n =∑ k=1 n l/(z−z nk ) withz nk ∈∂D, so that approximation in ∥ ∥ q ,q<-2, is not possible. In this paper, we give an order of estimate of ∥f−S n ∥ q for 2<q<∞ when ∂D is a sufficiently smooth Jordan curve, and prove that this order of approximation is in general best possible.

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Authors and Affiliations

  1. Center for Approximation Theory Department of Mathematics, Texas A&M University, 77843, College Station, Texas, USA

    Charles K. Chui

  2. Department of Mathematics, Peking University, Beijing, China

    Xie-Chang Shen

Authors
  1. Charles K. Chui
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  2. Xie-Chang Shen
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Communicated by J. Milne Anderson and Paul Nevai.

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Chui, C.K., Shen, XC. Order of approximation by electrostatic fields due to electrons. Constr. Approx 1, 121–135 (1985). https://doi.org/10.1007/BF01890026

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  • DOI: https://doi.org/10.1007/BF01890026

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