论文标题
关键CR GJM操作员的分析
Analysis of the critical CR GJMS operator
论文作者
论文摘要
严格的pseudoconvex cr歧管上的临界CR GJMS运算符是非避风行明的CR不变差分运算符。我们证明，在嵌入性假设下，它本质上是自动化的，并且具有封闭范围。此外，它的频谱是离散的，与每个非零特征值相对应的特征空间是光滑函数空间的有限维子空间。作为应用程序，我们获得了存在零Cr $ Q $ curvature的联系表的必要条件。
The critical CR GJMS operator on a strictly pseudoconvex CR manifold is a non-hypoelliptic CR invariant differential operator. We prove that, under the embeddability assumption, it is essentially self-adjoint and has closed range. Moreover, its spectrum is discrete, and the eigenspace corresponding to each non-zero eigenvalue is a finite-dimensional subspace of the space of smooth functions. As an application, we obtain a necessary and sufficient condition for the existence of a contact form with zero CR $Q$-curvature.
