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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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), 351-391 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), 351-391
  • MSC: Primary 22E25; Secondary 22E45, 22E46
  • DOI: https://doi.org/10.1090/S0002-9947-1991-1043858-7
  • MathSciNet review: 1043858