论文标题
团体保存运营商的结构
The structure of group preserving operators
论文作者
论文摘要
在本文中，我们证明了在$ l^2（\ mathfrak {s}）$的子空间上定义的普通有限运算符的特定对角线化，其中$ \ mathfrak {s} $是第二个可数的LCA组。在集团$γ$的作用下，《运营商法》不变的子空间是$ \ mathfrak {s} $的均匀晶格的半导体产品，并具有离散的自动形态组。该类包括在应用程序作为图像模型中很重要的晶体组。假定操作员是$γ$保存。即，他们以$γ$的行动上下班。特别是我们为这些操作员获得光谱分解。这将最新的结果概括为在晶格不变子空间上作用于$ \ mathfrak {s} $的euclidean空间。
In this paper, we prove the existence of a particular diagonalization for normal bounded operators defined on subspaces of $L^2(\mathfrak{S})$ where $\mathfrak{S}$ is a second countable LCA group. The subspaces where the operators act are invariant under the action of a group $Γ$ which is a semi-direct product of a uniform lattice of $\mathfrak{S}$ with a discrete group of automorphisms. This class includes the crystal groups which are important in applications as models for images. The operators are assumed to be $Γ$ preserving. i.e. they commute with the action of $Γ$. In particular we obtain a spectral decomposition for these operators. This generalizes recent results on shift-preserving operators acting on lattice invariant subspaces where $\mathfrak{S}$ is the Euclidean space.
