Order of approximation by electrostatic fields due to electrons |
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| Authors: | Charles K Chui Xie-Chang Shen |
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| Institution: | 1. Center for Approximation Theory Department of Mathematics, Texas A&M University, 77843, College Station, Texas, USA
2. Department of Mathematics, Peking University, Beijing, China
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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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