Journal of Functional Analysis ( IF 1.7 ) Pub Date : 2021-02-20 , DOI: 10.1016/j.jfa.2021.108960 Yuanan Diao , Deguang Han , Zhongyan Li
Functional Gabor single-frame or multi-frame generator multipliers are the matrices of function entries that preserve Parseval Gabor single-frame or multi-frame generators. An interesting and natural question is how to characterize all such multipliers. This question has been answered for several special cases including the case of single-frame generators in two dimensions and the case of multi-frame generators in one-dimension. In this paper we completely characterize multipliers for Gabor single-frame and multi-frame generators with respect to separable time-frequency lattices in any given dimension. Our approach is general and applies to the previously known cases as well.
中文翻译:
任何给定维度的Gabor单帧和多帧乘法器
功能Gabor单帧或多帧生成器乘法器是保留Parseval Gabor单帧或多帧生成器的函数条目矩阵。一个有趣而自然的问题是如何表征所有这样的乘数。对于几种特殊情况,已经回答了这个问题,其中包括二维的单帧生成器和一维的多帧生成器。在本文中,我们针对任意给定维度中可分离的时频晶格,完全描述了Gabor单帧和多帧生成器的乘法器。我们的方法是通用的,并且也适用于先前已知的情况。