发表机构
New Jersey Institute of Technology（新泽西理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究刻画了二阶B样条$Q_2$的Zak变换零点集，证明沿$ab=1/q$双曲线的Gabor框架阻碍尖锐，解决了Lemvig等人的未决问题。
AI 中文摘要
我们对二阶B样条$Q_2$的Zak变换的零点集给出了完整刻画。由此，我们得到了Lemvig-Nielsen对$Q_2$的Gabor框架性质的阻碍的新证明；沿双曲线$ab=1/q$，我们证明这些阻碍是尖锐的：它们未排除的每个点都属于框架集。这给出了该族中整条曲线上$\boldsymbol{\textit{F}}(Q_2)$的首个完整刻画，解决了Lemvig和Nielsen在文献\textbf{\textit{[Lemniel]}}中留下的未决问题。
英文摘要
We give a complete characterization of the zero set of the Zak transform of the second-order B-spline $Q_2$. As a consequence, we obtain a new proof of the Lemvig--Nielsen obstructions to the Gabor frame property of $Q_2$, and, along the hyperbola $ab=1/q$, we show these obstructions are sharp: every point they do not exclude belongs to the frame set. This gives the first complete characterization of $\mathcal F(Q_2)$ along an entire curve in this family, resolving a question left open by Lemvig and Nielsen.
