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Springer Monographs in Mathematics

Discrete Energy on Rectifiable Sets

Authors: Borodachov, Sergiy V., Hardin, Douglas P., Saff, Edward B

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  • Subject matter connects several different branches of mathematics and has myriad applications to the physical and biological sciences
  • Book is rich with attractive, full color images
  • Self-contained book, accessible to both research professionals and graduate students
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eBook $109.00
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  • ISBN 978-0-387-84808-2
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  • Immediate eBook download after purchase
Hardcover $149.99
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  • ISBN 978-0-387-84807-5
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  • Usually dispatched within 3 to 5 business days.
About this book

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.

About the authors

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.

 

Table of contents (15 chapters)

Table of contents (15 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-0-387-84808-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-0-387-84807-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Discrete Energy on Rectifiable Sets
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2019
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC, part of Springer Nature
eBook ISBN
978-0-387-84808-2
DOI
10.1007/978-0-387-84808-2
Hardcover ISBN
978-0-387-84807-5
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XVIII, 666
Number of Illustrations
9 b/w illustrations, 53 illustrations in colour
Topics