Abstract
Let \(\textsf {G}\) be a Carnot group of homogeneous dimension M and \(\Delta \) its horizontal sublaplacian. For \(\alpha \in (0,M)\) we show that operators of the form \(H_\alpha :=(-\Delta )^\alpha +V\) have no singular spectrum, under generous assumptions on the multiplication operator V. The proof is based on commutator methods and Hardy inequalities.
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The author has been supported by Proyecto Fondecyt 1160359.
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Măntoiu, M. Spectral analysis for perturbed operators on Carnot groups. Arch. Math. 109, 167–177 (2017). https://doi.org/10.1007/s00013-017-1037-0
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DOI: https://doi.org/10.1007/s00013-017-1037-0