铺砌、填充与施瓦茨类加伯窗的存在性
Tilings, packings, and the existence of Schwartz-class Gabor windows
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中文总结 AI 辅助
该研究解决时频分析中格加伯框架施瓦茨类窗的存在性问题，刻画相关格类并推导精确融合Balian-Low定理，还构造了可紧支撑的光滑窗。
中文摘要 AI 辅助
格加伯框架的施瓦茨类窗的存在性与构造是时频分析的核心问题。针对一般时频格，我们精确刻画了那些容许施瓦茨类窗且还容许Feichtinger代数中窗的格，由此得到了R^d中格的精确融合Balian-Low定理。针对可分格与指定的块零形式，我们构造了在时间或频率上紧支撑的光滑窗，这些构造基于对两类格对的刻画：存在单个集合，其与其中一个格铺砌，且其ε邻域与另一个格填充。
英文摘要
The existence and construction of Schwartz-class windows for lattice Gabor frames is a central problem in time--frequency analysis. For general time--frequency lattices, we characterize exactly those lattices that admit Schwartz-class windows and, additionally, windows in the Feichtinger algebra. Thereby we arrive at sharp classical and amalgam Balian--Low theorems for lattices in $\mathbb{R}^d$. For separable lattices and specified block-zero forms, we construct smooth windows that are compactly supported either in time or in frequency. These constructions are based on a characterization of pairs of lattices for which there exists a single set that tiles with one lattice and whose $\varepsilon$-neighborhood packs with the other.
