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Electrostatics, Hyperbolic Geometry and Wandering Vectors
Author(s) -
Grinshpan Anatolii
Publication year - 2004
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s002461070300485x
Subject(s) - planar , geometry , hyperbolic geometry , electrostatics , mathematics , differential geometry , physics , computer science , quantum mechanics , computer graphics (images)
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.