A Paley-Wiener Theorem for the Spherical Transform Associated with the Generalized Gelfand Pair (U(p,q),H_n), p+q=n - Campos, Silvina (MATHEMATICA SCANDINAVICA, 2016)
In this work we prove a Paley-Wiener theorem for the spherical transform associated to the generalized Gelfand pair (H_nU(p,q),H_n), 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 Σ of R^2, we prove that the restrictions of the spherical transforms of functions in C_0^∞(H_n) to appropriated subsets of Σ, can be extended to holomorphic functions on C^2. Also, we obtain a real variable characterizations of such transforms.