A PALEY-WIENER THEOREM FOR THE SPHERICAL TRANSFORM ASSOCIATED WITH THE GENERALIZED GELFAND PAIR (U(p, q), H-n), p plus q = n

作者：Campos Silvina^*

来源：Mathematica Scandinavica, 2016, 119(2): 249-282.

In this work we prove a Paley-Wiener theorem for the spherical transform associated to the generalized Gelfand pair (H-n x U (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 Sigma of R-2, we prove that the restrictions of the spherical transforms of functions in C-0(infinity) (H-n) to appropriated subsets of Sigma, can be extended to holomorphic functions on C-2. Also, we obtain a real variable characterizations of such transforms.

• 出版日期2016