Spectral Analysis for Perturbed Operators on Carnot Groups

Let $\G$ be a Carnot group of homogeneous dimension $M$ and $Δ$ its horizontal sublaplacian. For $α\in(0,M)$ we show that operators of the form $H_α:=(-Δ)^α+V$ 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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