框架小波乘子在正交小波集合和框架小波集合研究包括其子类的拓扑性质和结构性质以及新小波的构造研究中均发挥着重要的作用。项目拟针对目前国内外框架小波乘子研究中存在的主要问题，采用算子代数的相关理论和方法，分别开展L^2(R^d)(d>=1)上多框架乘子刻画的系统化和特定群表示酉系框架乘子的拓展研究。在L^2(R^d)上，重点对多正交小波乘子、多Parseval框架乘子、Super框架乘子、多Garbor框架乘子、单和多Riesz框架乘子进行刻画研究，并揭示各类多框架乘子间的内在关系包括等价性，从而促进该空间框架小波乘子刻画理论的系统化。在群表示酉系上，主要研究特定群表示的具体向量乘子刻画，包括有限群、ICC群、交换群等群表示的多游荡向量乘子、有限群表示的Parseval Super-框架乘子刻画，以丰富和发展群表示框架向量乘子的相关理论。

Frame wavelet multipliers play important roles in characterizing the structures and topological properties of the sets of all orthogonal wavelets and frame wavelets including their subsets, and also in structuring new frame wavelets. In this research proposal, We will focus on the new and important problems facing wavelet multipliers studies by using theories and methods relevant to operator algebras. The focal points will be put on the systematical characterization of multi-frame vector multipliers in L^2(R^d) and its extension to the specific frame vector multipliers for special group representation unitary systems. In L^2(R^d), we will characterize multi-orthogonal wavelet multipliers, Parseval multi-frame multipliers, Super-frame multipliers, multi-Garbor frame multipliers, single and multi-Riesz frame multipliers and reveal their relations including equivalence in order to facilitate systematic research in this field. For group representation unitary systems, we will study the structures of multi wandering vector multipliers for special group representations including finite group, ICC group and abelian group, the single Parseval Super-frame vector multipliers for finite group respectively in order to develop the theories related to frame vector multipliers.