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Mathematische Zeitschrift

, Volume 272, Issue 1–2, pp 483–496 | Cite as

Unitary representations of unimodular Lie groups in Bergman spaces

  • Giuseppe Della Sala
  • Joe J. Perez
Article

Abstract

For an arbitrary unimodular Lie group G, we construct strongly continuous unitary representations in the Bergman space of a strongly pseudoconvex neighborhood of G in the complexification of its underlying manifold. These representation spaces are infinite-dimensional and have compact kernels. In particular, the Bergman spaces of these natural manifolds are infinite-dimensional.

Mathematics Subject Classification (2000)

Primary 43A65 32W05 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität WienViennaAustria

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