A Paley-Wiener theorem for the Θ-spherical transform: the even multiplicity case

الأصل · EN

The 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 Dₘ 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.