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Spherical functions on Cartan motion groups


Author: Cary Rader
Journal: Trans. Amer. Math. Soc. 310 (1988), 1-45
MSC: Primary 22E45; Secondary 43A90
DOI: https://doi.org/10.1090/S0002-9947-1988-0965746-4
MathSciNet review: 965746
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Abstract: This paper gives a reasonably complete treatment of harmonic analysis on Cartan motion groups. Included is an explicit parameterization of irreducible spherical functions of general $ K$-type, and of the nonunitary dual (and its topology). Also included is the explicit Plancherel measure, the Paley Wiener theorem, and an asymptotic expansion of general matrix entries. (These are generalized Bessel functions.) However the main result is Theorem 19, a technical result which measures the size of the centralizer of $ K$ in the universal enveloping algebra of the corresponding reductive group.


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DOI: https://doi.org/10.1090/S0002-9947-1988-0965746-4
Article copyright: © Copyright 1988 American Mathematical Society

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