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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