论文标题
$ \ mathbb {z}^n $上的伪差异操作员的基本伴奏
The essential adjointness of pseudo-differential operators on $\mathbb{Z}^n$
论文作者
论文摘要
在晶格$ \ mathbb {z}^n $的设置中，我们考虑了一个伪分别的操作员$ a $，其符号属于$ \ Mathbb {z}^n \ times \ times \ times \ mathbb {t}^n $，其中$ \ mathBb {我们意识到$ a $作为操作员在离散sobolev spaces之间作用$ h^{s_j}（\ m athbb {z}^n）$，$ s_j \ in \ in \ mathbb {r} $，$ j = 1,2 $，带有离散的schwartz space作为$ a $ a $ a $ a $ a $ a $ a的schwartz space。我们为对$（a，\，a^{\ dagger}）$的基本伴随提供了足够的条件，其中$ a^{\ dagger} $是$ a $的正式伴随。
In the setting of the lattice $\mathbb{Z}^n$ we consider a pseudo-differential operator $A$ whose symbol belongs to a class defined on $\mathbb{Z}^n\times \mathbb{T}^n$, where $\mathbb{T}^n$ is the $n$-torus. We realize $A$ as an operator acting between the discrete Sobolev spaces $H^{s_j}(\mathbb{Z}^n)$, $s_j\in\mathbb{R}$, $j=1,2$, with the discrete Schwartz space serving as the domain of $A$. We provide a sufficient condition for the essential adjointness of the pair $(A,\,A^{\dagger})$, where $A^{\dagger}$ is the formal adjoint of $A$.
