Spectral analysis for perturbed operators on Carnot groups

Abstract

© 2017, Springer International Publishing. Let G be a Carnot group of homogeneous dimension M and Δ its horizontal sublaplacian. For α∈ (0 , M) we show that operators of the form Hα: = (- 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.