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arXiv · 2011.09942

An uncertainty principle for spectral projections on rank one symmetric spaces of noncompact type

Pritam Ganguly·Sundaram Thangavelu
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Abstract

Let $G $ be a noncompact semisimple Lie group with finite centre. Let $X=G/K$ be the associated Riemannian symmetric space and assume that $X$ is of rank one. The spectral projections associated to the Laplace-Beltrami operator are given by $P_{\lambda}f =f\ast \Phi_{\lambda}$, where $\Phi_{\lambda}$ are the elementary spherical functions on $X$. In this paper, we prove an Ingham type uncertainty principle for $P_{\lambda}f$. Moreover, similar results are obtained in the case of spectral projections associated to Dunkl Laplacian.

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Pritam Ganguly, Sundaram Thangavelu. 2020-11-19. An uncertainty principle for spectral projections on rank one symmetric spaces of noncompact type. https://arxiv.org/abs/2011.09942

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