论文标题
Weyl-Heisenberg组的翻译和框架的非平稳帧和扩展仿射组
Nonstationary frames of translates and frames for the Weyl--Heisenberg group and the extended affine group
论文作者
论文摘要
在这项工作中，我们为Weyl-Heisenberg组和小波框架分析了扩展仿射组的小波框架。首先，我们为存在的非平稳框架提供了必要和充分的条件。使用这些条件，我们为扩展仿射组的Weyl--Heisenberg组和小波框架提供了Gabor框架的存在。我们在窗口函数的傅立叶变换方面呈现了函数的表示。我们表明，翻译框架的规范双重偶具有相同的结构。提出了翻译的非平稳框架框架操作员的倒数近似。结果表明，如果非平稳的翻译框架是riesz的基础，则它是线性独立的，并且满足逆帧运算符的近似。最后，我们为非平稳序列的翻译序列提供等效条件，为线性独立。
In this work, we analyze Gabor frames for the Weyl--Heisenberg group and wavelet frames for the extended affine group. Firstly, we give necessary and sufficient conditions for the existence of nonstationary frames of translates. Using these conditions, we give the existence of Gabor frames from the Weyl--Heisenberg group and wavelet frames for the extended affine group. We present a representation of functions in the closure of the linear span of a Gabor frame sequence in terms of the Fourier transform of window functions. We show that the canonical dual of frames of translates has the same structure. An approximation of inverse of the frame operator of nonstationary frames of translates is presented. It is shown that a nonstationary frame of translates is a Riesz basis if it is linearly independent and satisfies approximation of the inverse frame operator. Finally, we give equivalent conditions for a nonstationary sequence of translates to be linearly independent.
