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2 results

  • ELECTROSTATICS, HYPERBOLIC GEOMETRY AND WANDERING VECTORS

  • ANATOLII GRINSHPAN
  • Journal:
    Journal of the London Mathematical Society / Volume 69 / Issue 1 / February 2004
    Published online by Cambridge University Press:
    28 January 2004, pp. 169-182
    Print publication:
    February 2004

  • 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.