Multiplicity One for Representations Corresponding to Spherical Distribution Vectors of Class ρ

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Helminck, Aloysius G. and Helminck, Gerardus F. (2005) Multiplicity One for Representations Corresponding to Spherical Distribution Vectors of Class ρ. Acta Applicandae Mathematicae, 86 (1-2). pp. 21-48. ISSN 0167-8019

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Abstract:In this paper one considers a unimodular second countable locally compact group G and the homogeneous space X:=H\G, where H is a closed unimodular subgroup of G. Over X complex vector bundles are considered such that H acts on the fibers by a unitary representation with closed image. The natural action of G on the space of square integrable sections is unitary and possesses an integral decomposition in so-called spherical distributions of class ρ. The uniqueness of this decomposition can be characterized by a number of equivalent properties. Uniqueness is shown to hold for a class of semidirect products.
Item Type:Article
Copyright:© 2005 Springer
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/69570
Official URL:http://dx.doi.org/10.1007/s10440-005-0461-5
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Metis ID: 233470