Non-existence of radial eigenfunctions for the perturbed Heisenberg sublaplacian

2023/10/27 by Luca Fanelli, Fanelli, Luca, Haruya Mizutani +5
Mathematics · #Advanced Mathematical Physics Problems #Spectral Theory in Mathematical Physics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2310.18050

Abstract

We prove uniform resolvent estimates in weighted L²-spaces for radial solutions of the sublaplacian L on the Heisenberg group ℍ^d. The proofs are based on the multipliers methods, and strongly rely on the use of suitable multipliers and of the associated Hardy inequalities. The constants in our inequalities are explicit and depend only on the dimension d. As application of the method, we obtain some suitable smallness and repulsivity conditions on a complex radial potential V on ℍ^d such that L+V has no radial eigenfunctions.

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