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Electrostatics, Hyperbolic Geometry and Wandering Vectors

Grinshpan, Anatolii (2004) Electrostatics, Hyperbolic Geometry and Wandering Vectors. Journal of the London Mathematical Society, 69 . pp. 169-182. ISSN 0024-6107. doi:10.1112/S002461070300485X.

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A family of planar discrete electrostatic systems on the unit circle with finitely atomic external fields is considered. The geometry of particles in the external field yielding a given minimum energy configuration is studied. As an application, the wandering vectors of the shift operator in the Dirichlet spaces associated with finitely atomic measures are also studied. In particular, the zero locus of a wandering vector is discussed.

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Additional Information:© 2004 London Mathematical Society. Received 13 October 2001; revised 7 March 2003. The author is grateful to Professor Donald Sarason for guidance and insight. He thanks the referee of this paper for useful criticism.
Classification Code:2000 Mathematics Subject Classification: 31A99, 46E20, 78A30, 31A35
Record Number:CaltechAUTHORS:20110822-105740726
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:24974
Deposited By: Tony Diaz
Deposited On:23 Aug 2011 16:14
Last Modified:09 Nov 2021 16:28

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