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Discrete Energy on Rectifiable Sets

  • Sergiy V. Borodachov
  • Douglas P. Hardin
  • Edward B. Saff
Book

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff
    Pages 1-11
  3. Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff
    Pages 13-47
  4. Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff
    Pages 49-75
  5. Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff
    Pages 77-125
  6. Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff
    Pages 127-191
  7. Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff
    Pages 193-260
  8. Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff
    Pages 261-327
  9. Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff
    Pages 329-353
  10. Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff
    Pages 355-410
  11. Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff
    Pages 411-440
  12. Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff
    Pages 441-478
  13. Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff
    Pages 479-496
  14. Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff
    Pages 497-524
  15. Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff
    Pages 525-538
  16. Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff
    Pages 539-602
  17. Back Matter
    Pages 603-666

About this book

Introduction

This book aims to provide an introduction to the broad and dynamic subject of discrete energy problems and point configurations. Written by leading authorities on the topic, this treatise is designed with the graduate student and further explorers in mind. The presentation includes a chapter of preliminaries and an extensive Appendix that augments a course in Real Analysis and makes the text self-contained. Along with numerous attractive full-color images, the exposition conveys the beauty of the subject and its connection to several branches of mathematics, computational methods, and physical/biological applications.

This work is destined to be a valuable research resource for such topics as packing and covering problems, generalizations of the famous Thomson Problem, and classical potential theory in Rd. It features three chapters dealing with point distributions on the sphere, including an extensive treatment of Delsarte–Yudin–Levenshtein linear programming methods for lower bounding energy, a thorough treatment of Cohn–Kumar universality, and a comparison of 'popular methods' for uniformly distributing points on the two-dimensional sphere. Some unique features of the work are its treatment of Gauss-type kernels for periodic energy problems, its asymptotic analysis of minimizing point configurations for non-integrable Riesz potentials (the so-called Poppy-seed bagel theorems), its applications to the generation of non-structured grids of prescribed densities, and its closing chapter on optimal discrete measures for Chebyshev (polarization) problems.

 

Keywords

Discretization Energy Asymptotics Equilibrium Distributions Minimum Energy Approach Riesz Kernels Riesz s-energy computational methods physical and biological applications theoretical mathematics plum-pudding model discrete energy

Authors and affiliations

  • Sergiy V. Borodachov
    • 1
  • Douglas P. Hardin
    • 2
  • Edward B. Saff
    • 3
  1. 1.Department of MathematicsTowson UniversityTowsonUSA
  2. 2.Center for Constructive Approximation, Department of MathematicsVanderbilt UniversityNashvilleUSA
  3. 3.Center for Constructive Approximation, Department of MathematicsVanderbilt UniversityNashvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-84808-2
  • Copyright Information Springer Science+Business Media, LLC, part of Springer Nature 2019
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-84807-5
  • Online ISBN 978-0-387-84808-2
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • Buy this book on publisher's site