DECOMPOSITION OF HARDY FUNCTIONS INTO SQUARE INTEGRABLE WAVELETS OF CONSTANT SHAPE
DECOMPOSITION OF HARDY FUNCTIONS INTO SQUARE INTEGRABLE WAVELETS OF CONSTANT SHAPE
复制标题
DOI：
10.1137/0515056
复制
发表时间：
1984-01-01
影响因子：
2
通讯作者：
MORLET, J
中科院分区：
文献类型：
--
作者：
GROSSMANN, A;MORLET, J
一个任意的平方可积实值函数（或者等价地，相关的哈代函数）可以方便地被分析成一个合适的常数形状的平方可积小波族（即通过其中任何一个的移位和伸缩获得）。如果小波满足这里给出的“容许条件”，则所得到的积分变换是等距的和自互反的。在一个特定的分析家庭的情况下，发挥类似的作用，相干态（Gabor小波）在通常的理论，得到明确的表达式。它们是根据介绍和研究的修改函数编写的。本文从群论的观点出发，研究了非幺模群的不可约表示的平方可积系数。
An arbitrary square integrable real-valued function (or, equivalently, the associated Hardy function) can be conveniently analyzed into a suitable family of square integrable wavelets of constant shape, (i.e. obtained by shifts and dilations from any one of them.) The resulting integral transform is isometric and self-reciprocal if the wavelets satisfy an “admissibility condition” given here. Explicit expressions are obtained in the case of a particular analyzing family that plays a role analogous to that of coherent states (Gabor wavelets) in the usual-theory. They are written in terms of a modified-function that is introduced and studied. From the point of view of group theory, this paper is concerned with square integrable coefficients of an irreducible representation of the nonunimodular-group.