论文标题
傅立叶 - 斯泰尔杰斯转换由局部紧凑组的诱导表示定义
Fourier-Stieltjes transform defined by induced representation on locally compact groups
论文作者
论文摘要
在这项工作中，我们将矢量度量的傅立叶变换和紧凑组定义的连续函数扩展到局部紧凑的组。 To do so, we consider a representation L of a normal compact subgroup K of a locally compact group G, and we use a representation of G induced by that of L. Then, we define the Fourier-Stieltjes transform of a vector measure and that of a continuous function with compact support defined on G from the representation of G. Then, we extend the Shur orthogonality relation established for compact groups to locally compact groups by using the representations of G由其正常的紧凑型亚组之一的统一表示。此扩展使我们能够以线性，连续且可逆的串联形式开发傅立叶式变换。
In this work we extend the Fourier-Stieltjes transform of a vector measure and a continuous function defined on compact groups to locally compact groups. To do so, we consider a representation L of a normal compact subgroup K of a locally compact group G, and we use a representation of G induced by that of L. Then, we define the Fourier-Stieltjes transform of a vector measure and that of a continuous function with compact support defined on G from the representation of G. Then, we extend the Shur orthogonality relation established for compact groups to locally compact groups by using the representations of G induced by the unitary representations of one of its normal compact subgroups. This extension enables us to develop a Fourier-Stieltjes transform in series form that is linear, continuous, and invertible.
