论文标题
局部紧凑型组的多态性
Polyhomomorphisms of locally compact groups
论文作者
论文摘要
让$ g $和$ h $是本地紧凑的团体，具有固定的两侧不变性HAAR措施。多形肌形态$ g \ to H $是固定HAAR措施的封闭子组$ r \ subset g \ times h $，其边际上的$ g $和$ h $由$ g $和$ h $的HAAR措施主导。多态性可以看作是配备“统一”度量的集合的多值地图发送点。对于polyHomorphsisms $ g \ to H $，$ h \ to K $，有一个定义明确的产品$ g \ to K $。相对于chabauty--bourbaki拓扑，$ g \ to h $的一组多态性$ g \ to h $是一个可元的紧凑空间，而bourbaki拓扑是分别连续的。多形肌形态$ g \ to h $确定一个规范操作员$ l^2（h）\至l^2（g）$，这是局部静脉测定到标量因子。例如，我们考虑在有限的磁场上局部紧凑的无限二维线性空间，并检查多态分类中线性算子组的封闭。
Let $G$ and $H$ be locally compact groups with fixed two-side-invariant Haar measures. A polyhomomorphism $G\to H$ is a closed subgroup $R\subset G\times H$ with a fixed Haar measure, whose marginals on $G$ and $H$ are dominated by the Haar measures on $G$ and $H$. A polyhomomorphism can be regarded as a multi-valued map sending points to sets equipped with 'uniform' measures. For polyhomomorphsisms $G\to H$, $H\to K$ there is a well-defined product $G\to K$. The set of polyhomomorphisms $G\to H$ is a metrizable compact space with respect to the Chabauty--Bourbaki topology and the product is separately continuous. A polyhomomorphism $G\to H$ determines a canonical operator $L^2(H)\to L^2(G)$, which is a partial isometry up to scalar factor. As an example, we consider locally compact infinite-dimensional linear spaces over finite fields and examine closures of groups of linear operators in semigroups of polyendomorphisms.
