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arXiv · 2301.05304

A characterization of the $L^2$-range of the Poisson transforms on a class of vector bundles over the quaternionic hyperbolic spaces

Abdelhamid Boussejra·Achraf Ouald Chaib
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Abstract

We study the $L^2$-boundedness of the Poisson transforms associated to the homogeneous vector bundles $ Sp(n,1)\times_{Sp(n)\times Sp(1)} V_\tau$ over the quaternionic hyperbolic spaces $ Sp(n,1)/Sp(n)\times Sp(1)$ associated with irreducible representations $\tau$ of $ Sp(n)\times Sp(1)$ which are trivial on $ Sp(n)$. As a consequence, we describe the image of the section space $L^2(Sp(n,1)\times_{Sp(n)\times Sp(1)} V_\tau)$ under the generalized spectral projections associated to a family of eigensections of the Casimir operator.

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Abdelhamid Boussejra, Achraf Ouald Chaib. 2023-01-12. A characterization of the $L^2$-range of the Poisson transforms on a class of vector bundles over the quaternionic hyperbolic spaces. https://arxiv.org/abs/2301.05304

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