论文标题
海森贝格sublaplacian的非自我伴侣扰动
Non self-adjoint perturbations of the Heisenberg sublaplacian
论文作者
论文摘要
我们证明了Sublaplacian $ \ Mathcal {l} $在Heisenberg Group $ \ Mathbb {H}^d $上的加权$ l^2 $ spaces中的统一分解估计。证明是基于乘数方法，并且强烈依赖于水平乘数和相关的耐力不平等的使用。我们不平等的常数是明确的，仅取决于尺寸$ d $。作为此方法的应用，我们在$ \ Mathbb {h}^d $上获得了复杂电势$ v $上的一些适当的较小和排斥性条件，以使$ \ mathcal {l}+v $的光谱不包含特定值。
We prove uniform resolvent estimates in weighted $L^2$-spaces for the sublaplacian $\mathcal{L}$ on the Heisenberg group $\mathbb{H}^d$. 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 $\mathbb{H}^d$ such that the spectrum of $\mathcal{L}+V$ does not contain eigenvalues.
