Ganguly, Pritam; Thangavelu, Sundaram An uncertainty principle for spectral projections on rank one symmetric spaces of noncompact type. (English) Zbl 1496.43005 Ann. Mat. Pura Appl. (4) 201, No. 1, 289-311 (2022). The authors present a weaker version of Chernoff’s theorem for Bessel and Jacobi operators. This result is used to prove a refined version of Ingham’s theorem for the Helgason Fourier transform on rank one Riemannian symmetric spaces of noncompact type. The authors also prove an Ingham type uncertainty principle for the generalized spectral projections associated to the Laplace-Beltrami operator. Similar Ingham type results for the generalized spectral projections associated to Dunkl Laplacian are also discussed. Reviewer: Ashish Bansal (Delhi) Cited in 3 Documents MSC: 43A85 Harmonic analysis on homogeneous spaces 43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups 22E30 Analysis on real and complex Lie groups 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) Keywords:Chernoff’s theorem; Riemannian symmetric spaces; Helgason Fourier transform; Dunkl transform; Ingham’s theorem; spectral projections PDFBibTeX XMLCite \textit{P. Ganguly} and \textit{S. Thangavelu}, Ann. Mat. Pura Appl. (4) 201, No. 1, 289--311 (2022; Zbl 1496.43005) Full Text: DOI arXiv Link References: [1] S. Bagchi, P. Ganguly, J. Sarkar and S. Thangavelu, On theorems of Chernoff and Ingham on the Heisenberg group (2020). arXiv:2009.14230 [2] Ben Said, S.; Orsted, B., Analysis on flat symmetric spaces, J. de Math. 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