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Discrete Energy on Rectifiable Sets (Hardcover, 1st ed. 2019)
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Discrete Energy on Rectifiable Sets (Hardcover, 1st ed. 2019)
Series: Springer Monographs in Mathematics
Expected to ship within 10 - 15 working days
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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.
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