Zeta distributions and boundary values of poisson transforms

摘要

Let G be the conformal group of a non-Euclidean Jordan algebra and let P be the maximal parabolic subgroup canonically associated to G. Standard intertwining operators between spherical degenerate principal series induced from P determine Zeta distributions. In this article, we obtain a functional equations for Zeta distributions by considering boundary values of Poisson transforms. We relate the constant occurring in the Zeta functional equation to that occurring in the functional equation of Wallach's Generalized Jacquet functionals. (C) 2004 Elsevier Inc. All rights reserved.