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

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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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Functional Analysis, 33C67, 43A90, 43A85

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http://salesiana.dossiersoluciones.com/handle/123456789/67215

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0304361
 http://arxiv.org/abs/math/0304361

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arXiv