A minimum energy problem and Dirichlet spaces

Grinshpan, Anatolii

doi:10.1090/S0002-9939-01-06029-4

A minimum energy problem and Dirichlet spaces
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Proc. Amer. Math. Soc. 130 (2002), 453-460 Request permission

Abstract:

We analyze a minimum energy problem for a discrete electrostatic model in the complex plane and discuss some applications. A natural characteristic distinguishing the state of minimum energy from other equilibrium states is established. It enables us to gain insight into the structure of positive trigonometric polynomials and Dirichlet spaces associated with finitely atomic measures. We also derive a related family of linear second order differential equations with polynomial solutions.

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