论文标题
Klein-Gordon类型运算符上渐近静态静态型操作员的基本自我相关性
Essential self-adjointness for the Klein-Gordon type operators on asymptotically static spacetime
论文作者
论文摘要
令$ x = \ mathbb {r} \ times m $为时空，其中$ m $是装有riemannian公制$ g $的封闭式歧管，我们考虑对称对称的klein-gordon型运算符$ x $上的$ p $ p $ p $ p $ p $ p $ p $ x $，这是$ \ partial_t^2- $ $ \ try^$ trian for $ \ trian trian trian f | $ \ triangle_g $是$ m $上的Laplace-Beltrami操作员。我们证明$ C_0^\ infty（x）$上的$ p $的基本自动化。证明的想法与作者最近的一篇论文密切相关，该论文就渐近平坦空间上克莱因·戈登操作员的基本自我与色性而言。
Let $X=\mathbb{R}\times M$ be the spacetime, where $M$ is a closed manifold equipped with a Riemannian metric $g$, and we consider a symmetric Klein-Gordon type operator $P$ on $X$, which is asymptotically converges to $\partial_t^2-\triangle_g$ as $|t|\to\infty$, where $\triangle_g$ is the Laplace-Beltrami operator on $M$. We prove the essential self-adjointness of $P$ on $C_0^\infty(X)$. The idea of the proof is closely related to a recent paper by the authors on the essential self-adjointness for Klein-Gordon operators on asymptotically flat spaces.
