A Paley-Wiener Theorem for the Spherical Transform Associated with the Generalized Gelfand Pair (U(p,q),Hn), p+q=n
DOI:
https://doi.org/10.7146/math.scand.a-24746Abstract
In this work we prove a Paley-Wiener theorem for the spherical transform associated to the generalized Gelfand pair (Hn⋉, where H_n is the 2n+1-dimensional Heisenberg group.
In particular, by using the identification of the spectrum of (U(p,q),H_n) with a subset \Sigma of \mathbb{R}^2, we prove that the restrictions of the spherical transforms of functions in C_{0}^{\infty}(H_n) to appropriated subsets of \Sigma, can be extended to holomorphic functions on \mathbb{C}^2. Also, we obtain a real variable characterizations of such transforms.
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Published
2016-11-01
How to Cite
Campos, S. (2016). A Paley-Wiener Theorem for the Spherical Transform Associated with the Generalized Gelfand Pair (U(p,q),H_{n}), p+q=n. MATHEMATICA SCANDINAVICA, 119(2), 249–282. https://doi.org/10.7146/math.scand.a-24746
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