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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A minimum energy problem and Dirichlet spaces


Author: Anatolii Grinshpan
Journal: Proc. Amer. Math. Soc. 130 (2002), 453-460
MSC (2000): Primary 31A99, 46E20, 78A30, 31A35
Published electronically: May 25, 2001
MathSciNet review: 1862125
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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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Additional Information

Anatolii Grinshpan
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Email: tolya@math.berkeley.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06029-4
PII: S 0002-9939(01)06029-4
Keywords: Electrostatic equilibrium, Dirichlet spaces, Lam\'{e} differential equation
Received by editor(s): January 18, 2000
Received by editor(s) in revised form: June 22, 2000
Published electronically: May 25, 2001
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2001 American Mathematical Society