2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67215The $Θ$-spherical functions generalize the spherical functions on Riemannian symmetric spaces and the spherical functions on non-compactly causal symmetric spaces. In this article we consider the case of even multiplicity functions. We construct a differential shift operator $D_m$ with smooth coefficients which generates the $Θ$-spherical functions from finite sums of exponential functions. We then use this fact to prove a Paley-Wiener theorem for the $Θ$-spherical transfrom.Functional Analysis33C67, 43A90, 43A85text