Characterization of Wilson Systems for General Lattices
Characterization of Wilson Systems for General Lattices
复制标题
一般格子威尔逊系统的表征
DOI：
--
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
P. Wojdyllo
中科院分区：
文献类型：
--
作者：
P. Wojdyllo
Wilson标准正交基是由Daubechies，Jaffard和Quinne在1991年使用冗余度为2的Gabor紧框架的元素组合构造的。在1994年，Auscher给出了Wilson系统是标准正交基的原子的特征。最近，Kutyniok和Strohmer将Wilson系统的概念推广到生成矩阵为Hermite标准形的格上。我们将他们的结果推广到体积为1/2的一般格上的Wilson标准正交基的充分刻画。此外，通过适当的符号修改，我们将这一结果推广到不同于经典Wilson系统的其他形式。
The Wilson orthonormal basis was constructed in 1991 by Daubechies, Jaffard and Journe using combinations of elements of Gabor tight frame with redundancy 2. In 1994, Auscher gave a characterization of the atoms for which the Wilson system is an orthonormal basis. Recently, Kutyniok and Strohmer generalized the notion of the Wilson system to the lattices whose generator matrix is in Hermite normal form. We extend their result to the full characterization of Wilson orthonormal bases on the general lattice of volume 1/2. Moreover, we generalize this result to other forms of Wilson systems differing from the classical one by the appropriate sign modification.