论文标题
表示理论和多级过滤器
Representation theory and multilevel filters
论文作者
论文摘要
我们提出了一个通用设置，可以在其中定义小波过滤器和多分辨率分解，而不是经典的$ \ mathbf l^2（\ mathbb r，dx）$设置。这是在{\ em Iterated功能系统}（IFS）测量的框架中完成的；其中包括到目前为止研究的所有案例，尤其是朱莉娅设定/衡量案例。每个IFS都有固定的订单，例如$ n $，我们表明小波过滤器是由$ x $的无限尺寸组$ g $从$ x $索引到统一组$ u_n $的。由于单位圆圈的特殊情况，我们称$ g $为循环组。
We present a general setting where wavelet filters and multiresolution decompositions can be defined, beyond the classical $\mathbf L^2(\mathbb R,dx)$ setting. This is done in a framework of {\em iterated function system} (IFS) measures; these include all cases studied so far, and in particular the Julia set/measure cases. Every IFS has a fixed order, say $N$, and we show that the wavelet filters are indexed by the infinite dimensional group $G$ of functions from $X$ into the unitary group $U_N$. We call $G$ the loop group because of the special case of the unit circle.
