论文标题
在光滑的紧凑型波数据包上，适应频率空间的瓷砖
On frames of smooth, compactly-supported wave packets adapted to tilings of frequency space
论文作者
论文摘要
我们建立了频率空间可接受的瓷砖的广泛概念，该概念将相关的波数据包框架与光滑和紧凑的元素相关。该框架旨在允许瓷砖几何形状，这些几何形状受到缩小的需求，这些几何形状在傅立叶侧可容纳施瓦茨的尾巴，并且超出了从Gabor到小波型分解的常见几何形状规模。该方法建立在Hernández，Labate和Weiss和Labate，Weiss和Wilson的技术基础上，以及Ingham的经典结果，表征了可获得紧凑型支持功能的最佳傅立叶衰减。
We establish a broad notion of admissible tilings of frequency space which admit associated wave packet frames with elements which are smooth and compactly supported. The framework is designed to allow for tile geometries which are minimally constrained by the need to accommodate Schwartz tails on the Fourier side and goes beyond the usual scale of geometries ranging from Gabor to wavelet-type decompositions. The approach builds on techniques of Hernández, Labate and Weiss and Labate, Weiss, and Wilson as well as a classical result of Ingham characterizing the best-possible Fourier decay for functions of compact support.
