Abstract
On rank one Riemannian symmetric spaces of noncompact type, which accommodates all hyperbolic spaces, we show that characterization of the eigenfunctions/eigendistributions of the Laplace–Beltrami operator, through the action of the heat operator is possible only when we confine in a small time. The results are different from their counter parts in the Euclidean spaces. All results and their proofs extend to Damek–Ricci spaces.
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The authors would like to thank the referees whose suggestions and criticism helped to improve the exposition.
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Communicated by Karlheinz Grochenig.
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Naik, M., Sarkar, R.P. Characterization of eigenfunctions of the Laplace–Beltrami operator through heat propagation in small time. Monatsh Math 192, 883–903 (2020). https://doi.org/10.1007/s00605-020-01437-0
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DOI: https://doi.org/10.1007/s00605-020-01437-0