Minimizing measures on condensers of infinitely many plates
Abstract
The study deals with a minimal energy problem over noncompact classes of infinite dimensional vector measures in a locally compact space. The components are positive measures (charges) satisfying certain normalizing assumptions and supported by given closed sets (plates) with the sign +1 or -1 prescribed such that oppositely signed sets are mutually disjoint, and the interaction matrix for the charges corresponds to an electrostatic interpretation of a condenser. For all positive definite kernels satisfying Fuglede's condition of consistency between the weak* and strong topologies, sufficient conditions for the existence of equilibrium measures are established and properties of their uniqueness, vague compactness, and continuity are studied.
Keywords
Cite
@article{arxiv.1001.4369,
title = {Minimizing measures on condensers of infinitely many plates},
author = {Natalia Zorii},
journal= {arXiv preprint arXiv:1001.4369},
year = {2010}
}
Comments
22 pages