具有第n阶 Hermite 函数的 Gabor 系统及其 oversampling 大于n+1的非框 (frame) 系统
泛函分析
2025-10-01 v2 数学物理
math.MP
摘要
我们证明，Gabor系统关于晶格的充分密度条件并不总是充分的。这一结论源于零点 Zak transform如何决定整数 over-sampled Gabor 系统框属性的结果。
引用
@article{arxiv.2502.09510,
title = {Gabor systems with Hermite functions of order n and oversampling greater than n+1 which are not frames},
author = {Markus Faulhuber},
journal= {arXiv preprint arXiv:2502.09510},
year = {2025}
}
备注
Version 2 contains an extended introduction and a section with open problems and new examples. 16 pages, 7 figures. To appear in Sampling Theory, Signal Processing, and Data Analysis