کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8898517 | 1631456 | 2018 | 26 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Covering and separation of Chebyshev points for non-integrable Riesz potentials
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
For Riesz s-potentials K(x,y)=|xây|âs, s>0, we investigate separation and covering properties of N-point configurations ÏNâ={x1,â¦,xN} on a d-dimensional compact set AâRâ for which the minimum of âj=1NK(x,xj) is maximal. Such configurations are called N-point optimal Riesz s-polarization (or Chebyshev) configurations. For a large class of d-dimensional sets A we show that for s>d the configurations ÏNâ have the optimal order of covering. Furthermore, for these sets we investigate the asymptotics as Nââ of the best covering constant. For these purposes we compare best-covering configurations with optimal Rieszs-polarization configurations and determine the sth root asymptotic behavior (as sââ) of the maximal s-polarization constants. In addition, we introduce the notion of “weak separation” for point configurations and prove this property for optimal Riesz s-polarization configurations on A for s>dim(A), and for dâ1⩽s
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Complexity - Volume 46, June 2018, Pages 19-44
Journal: Journal of Complexity - Volume 46, June 2018, Pages 19-44
نویسندگان
A. Reznikov, E. Saff, A. Volberg,