标题： 半直积的连续小波变换：循环表示与Plancherel测度 显示英文标题

标题： Continuous wavelet transforms from semidirect products: Cyclic representations and Plancherel measure

摘要： 由向量群与矩阵群（所谓的膨胀群）的半直积的拟正则表示产生的连续小波变换已经被许多作者研究过。 最近，注意力从不可约情形转移到了更一般的膨胀群，例如循环群（更一般地：离散群）或单参数群。 这些群不会产生不可约平方可积表示，但仍然可以（且相当简单）为一大类群给出可允许性条件。 我们通过建立与半直积的Plancherel理论的联系，将这些结果置于理论背景中，并展示可允许性条件如何与使用Plancherel理论的抽象可允许性条件相关联。 显示英文摘要

摘要： Continuous wavelet transforms arising from the quasiregular representation of a semidirect product of a vector group with a matrix group -- the so-called dilation group -- have been studied by various authors. Recently the attention has shifted from the irreducible case to include more general dilation groups, for instance cyclic (more generally: discrete) or one-parameter groups. These groups do not give rise to irreducible square-integrable representations, yet it is possible (and quite simple) to give admissibility conditions for a large class of them. We put these results in a theoretical context by establishing a connection to the Plancherel theory of the semidirect products, and show how the admissibility conditions relate to abstract admissibility conditions which use Plancherel theory.