Discrete Energy on Rectifiable Sets

Sergiy V. Borodachov is a Professor of Mathematics at Towson University, which he joined in 2008. Prof. Borodachov's primary research interests include approximation theory, numerical analysis, and minimal energy problems. He authored or co-authored more than 30 research articles and gave more than 90 talks at research conferences and seminars. Douglas P. Hardin is a Professor of Mathematics and a Professor of Biomedical Informatics at Vanderbilt University.  His research interests include discrete minimum energy problems, fractals, harmonic analysis (wavelets), inverse problems, and machine learning.  Hardin has authored or co-authored over 115 research publications, 2 monographs, and co-edited 3 research journal special issues. Edward B. Saff is a Professor of Mathematics at Vanderbilt University and Director of the Center for Constructive Approximation. His research areas include approximation theory, numerical analysis, and potential theory. Saff is a Fellow of the American Mathematics Society, a Foreign Member of the Bulgarian Academy of Science, and was a recipient of both a Guggenheim and a Fulbright Fellowships. He has authored or co-authored over 270 research articles, 4 research monographs and 4 textbooks, and is co-Editor-in-Chief and Managing Editor of the research journal Constructive Approximation. Prof. Saff also serves on the boards of 3 other research journals.  

0. An Overview: Discretizing Manifolds via Particle Interactions.-1. Preliminaries.- 2. Basics of Minimal Energy.- 3.-Introduction to Packing and Covering.- 4. Continuous and Discrete Energy.- 5. LP Bounds on the Sphere.- 6. Asymptotics for Energy Minimizing Congurations on Sd.- 7. Some Popular Algorithms for Distributing Points on S2.- 8. Minimal Energy in the Hypersingular Case.-  9. Minimal Energy Asymptotics in the "Harmonic Series" Case.-  10. Periodic Riesz Energy.- 11. Congurations with non-Uniform Distribution.-  12. Low Complexity Energy Methods for Discretization.- 13. Best-Packing on Compact Sets.- 14. Optimal Discrete Measures for Potentials: Polarization (Chebyshev) Constants.- Appendix.- References.- List of Symbols.- Index.