标题： 辐射时空上波算子的本质自伴性 显示英文标题

标题： The essential self-adjointness of the wave operator on radiative spacetimes

摘要： 我们证明了达朗贝尔算子$\square_g$的本质自伴性，允许比以前考虑的更广泛的时空类，包括通过引力辐射扰动闵可夫斯基时空所产生的那些时空。 我们强调由Taira在密切相关设置中证明的事实，即所有满足$\square_g u = \lambda u +f$的缓增分布$u$对于$\lambda\in \mathbb{C}\backslash \mathbb{R}$和$f$范数而言都是 Schwartz 分布。 该证明是完全微局部的，并且由于第三作者最近开发的“de,sc-”工具而相对快速。 显示英文摘要

摘要： We prove the essential self-adjointness of the d'Alembertian $\square_g$, allowing a larger class of spacetimes than previously considered, including those that arise from perturbing Minkowski spacetime by gravitational radiation. We emphasize the fact, proven by Taira in closely related settings, that all tempered distributions $u$ satisfying $\square_g u = \lambda u +f$ for $\lambda\in \mathbb{C}\backslash \mathbb{R}$ and $f$ Schwartz are Schwartz. The proof is fully microlocal and relatively quick given the ``de,sc-'' machinery recently developed by the third author.