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

Gestur Olafsson·Angela Pasquale
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Abstract

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 $D_m$ 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.

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Gestur Olafsson, Angela Pasquale. 2003-04-23. A Paley-Wiener theorem for the $Θ$-spherical transform: the even multiplicity case. https://arxiv.org/abs/math/0304361

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