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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Homogeneous distributions on the Heisenberg group and representations of $ {\rm SU}(2,1)$


Author: R. C. Fabec
Journal: Trans. Amer. Math. Soc. 328 (1991), 351-391
MSC: Primary 22E25; Secondary 22E45, 22E46
MathSciNet review: 1043858
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Abstract: A 'Fourier' transform of tempered distributions on the Heisenberg group is defined to analyze homogeneous distributions relative the group of dilations $ (z,t) \mapsto (r\,z,{r^2}t)$, $ r \in {\mathbf{R}}$. An inversion formula is derived for the abelian central Fourier transform of the distribution. These formulas are applied to the family of homogeneous distributions defining the intertwining operators for the group $ {\text{SU}}(2,1)$. Explicit unitary structures are determined on subquotient representations and their spectral decompositions on the minimal parabolic subgroup are obtained.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1043858-7
PII: S 0002-9947(1991)1043858-7
Article copyright: © Copyright 1991 American Mathematical Society