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Spectral Analysis for Perturbed Operators on Carnot Groups (1606.04810v1)
Published 15 Jun 2016 in math.FA and math.SP
Abstract: Let $\G$ 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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