Homogeneous distributions on the Heisenberg group and representations of $\textrm {SU}(2,1)$
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 by R. C. Fabec PDF
 Trans. Amer. Math. Soc. 328 (1991), 351391 Request permission
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.References

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Additional Information
 © Copyright 1991 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 328 (1991), 351391
 MSC: Primary 22E25; Secondary 22E45, 22E46
 DOI: https://doi.org/10.1090/S00029947199110438587
 MathSciNet review: 1043858