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

2020/11/19 by Pritam Ganguly, Sundaram Thangavelu, Ganguly, Pritam +1 · 1 citation
Mathematics · #33C45 #43A25 #Advanced Algebra and Geometry #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Primary: 43A85 #Secondary:22E30

paper · pdf · doi:10.48550/arxiv.2011.09942

openalex publication_date 2020/11/19 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Let G be a noncompact semisimple Lie group with finite centre. Let X=G/K\nbe the associated Riemannian symmetric space and assume that X is of rank\none. The spectral projections associated to the Laplace-Beltrami operator are\ngiven by P_\λf =f\∗ \Φ_\λ, where \Φ_\λ are the\nelementary spherical functions on X. In this paper, we prove an Ingham type\nuncertainty principle for P_\λf. Moreover, similar results are\nobtained in the case of spectral projections associated to Dunkl Laplacian.\n

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