论文标题
Carnot群体和Schrödinger操作员光谱差距的庞加莱不平等现象
Poincaré inequalities on Carnot Groups and spectral gap of Schrödinger operators
论文作者
论文摘要
在这项工作中，我们提供了足够的条件，在此条件下，Carnot群体的全球庞加莱不平等现象是针对Lebesgue措施绝对连续的大型概率措施的正确条件。这种概率度量的密度是根据该组的均质准总结给出的。我们提供了适用条件在内的例子，包括最著名的Carnot群体家庭。特别是，这允许在先前的工作中扩展结果[CFZ21]。结果的结果是相关的Schrödinger运算符具有光谱差距。
In this work we give a sufficient condition under which the global Poincaré inequality on Carnot groups holds true for a large family of probability measures absolutely continuous with respect to the Lebesgue measure. The density of such probability measure is given in terms of homogeneous quasi-norm on the group. We provide examples to which our condition applies including the most known families of Carnot groups. This, in particular, allows to extend the results in the previous work [CFZ21]. A consequence of our result is that the associated Schrödinger operators have a spectral gap.
