Spectral analysis for perturbed operators on Carnot groups

DOI10.1007/s00013-017-1037-0zbMath1373.22016arXiv1606.04810OpenAlexW2963609804MaRDI QIDQ2407401

Marius Măntoiu

Publication date: 29 September 2017

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.04810

zbMATH Keywords

singular spectrumcommutatorinvariant differential operatorstratified Lie groupSublaplacian

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Analysis on real and complex Lie groups (22E30) Nilpotent and solvable Lie groups (22E25)

Cites Work

• Quantization on nilpotent Lie groups
• Some sharp Rellich type inequalities on nilpotent groups and applications
• On horizontal Hardy, Rellich, Caffarelli-Kohn-Nirenberg and \(p\)-sub-Laplacian inequalities on stratified groups
• Absence of singular continuous spectrum for certain self-adjoint operators
• Limiting absorption principle at critical values for the Dirac operator
• Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups
• Hardy and uncertainty inequalities on stratified Lie groups
• Spectral analysis for adjacency operators on graphs
• Spectral analysis for convolution operators on locally compact groups
• Absence of singular spectrum for Schrödinger operators with anisotropic potentials and magnetic fields
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• Smooth operators and commutators
• Spectral averaging, perturbation of singular spectra, and localization
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