论文标题
球体上的连续小波框架：重新审视组理论方法
Continuous Wavelet Frames on the Sphere: The Group-Theoretic Approach Revisited
论文作者
论文摘要
在\ cite {av99}中，Antoine和Vandergheynst提出了一种群体理论方法，用于在球体上连续小波框架。该框架是由单个所谓的可接受函数构建的，它通过应用与Lorentz组表示相关的单一操作员，该算子是iwasawa分解的nilpotent因子。我们证明了在球体上功能的必要条件，这确保相应的系统是框架。我们通过提供完整而详细的证明来加强\ cite {av99}的类似结果。
In \cite{AV99}, Antoine and Vandergheynst propose a group-theoretic approach to continuous wavelet frames on the sphere. The frame is constructed from a single so-called admissible function by applying the unitary operators associated to a representation of the Lorentz group, which is square-integrable modulo the nilpotent factor of the Iwasawa decomposition. We prove necessary and sufficient conditions for functions on the sphere, which ensure that the corresponding system is a frame. We strengthen a similar result in \cite{AV99} by providing a complete and detailed proof.
