Configurations with Nonuniform Distribution

  • Sergiy V. BorodachovEmail author
  • Douglas P. Hardin
  • Edward B. Saff
Part of the Springer Monographs in Mathematics book series (SMM)


In this chapter we discuss the following generalization of the minimal discrete energy problem. Let \((\subset \mathbb {R})\) be compact metric space and let \(w:A\times A\rightarrow [0,\infty ]\) be a given function which we will call the weight. For a given N-point configuration \(\omega _N=\{x_1,\ldots , x_N\}\) on A and a given number \(s>0\), define the (ws)-energy of \(\omega _N\) by \( E^w_s(\omega _N):=\sum \limits _{i=1}^{N}\sum \limits _{j=1\atop j\ne i}^{N}\frac{w(x_i, x_j)}{|x_i - x_j|^s}. \)

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Sergiy V. Borodachov
    • 1
    Email author
  • Douglas P. Hardin
    • 2
  • Edward B. Saff
    • 2
  1. 1.Department of MathematicsTowson UniversityTowsonUSA
  2. 2.Center for Constructive Approximation, Department of MathematicsVanderbilt UniversityNashvilleUSA

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