论文标题
Vilenkin组的小波集和广义缩放集
Wavelet Sets and Generalized Scaling Sets on Vilenkin Group
论文作者
论文摘要
对于Vilenkin群，仅知道与多分辨率分析（MRA）相关的多波网的存在。在本文中，我们表明，通过使用小波集，我们还可以在Vilenkin组的情况下构建单个小波，而Vilenkin组与MRA无关。我们对Vilenkin组上的单个和多波网组进行了表征。此外，我们研究了广义缩放集，它们的某些属性以及小波集和广义缩放集之间的关系。
For Vilenkin group only the existence of multiwavelets associated with multiresolution analysis (MRA) is known. In this paper, we have shown that by using wavelet sets we can also construct single wavelet in case of Vilenkin group which are not associated with MRA.We have given characterization of single and multi-wavelet sets on Vilenkin group. Further, we have studied generalized scaling sets, some of their properties and relation between wavelet sets and generalized scaling sets.
