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⋉U(p,q),Hn), where Hn is the 2n+1-dimensional Heisenberg group.
In particular, by using the identification of the spectrum of (U(p,q),Hn) with a subset Σ of R2, we prove that the restrictions of the spherical transforms of functions in C∞0(Hn) to appropriated subsets of Σ, can be extended to holomorphic functions on C2. 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),Hn), p+q=n. MATHEMATICA SCANDINAVICA, 119(2), 249–282. https://doi.org/10.7146/math.scand.a-24746
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