Non self-adjoint perturbations of the Heisenberg sublaplacian

2022/03/14 by Luca Fanelli, Fanelli, Luca, Luz Roncal +3
Mathematics · #47B28 #47F05 #81Q12 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary: 35R03 #Secondary: 47A10 #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2203.07296

openalex publication_date 2022/03/14 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

We prove uniform resolvent estimates in weighted L²-spaces for the sublaplacian L on the Heisenberg group ℍ^d. The proof are based on multiplier methods, and strongly rely on the use of horizontal multipliers and the associated Hardy inequalities. The constants of our inequalities are explicit and depend only on the dimension d. As applications of this method, we obtain some suitable smallness and repulsivity conditions on a complex potential V on ℍ^d such that the spectrum of L+V does not contain eigenvalues.

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