Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Stangl, Alexander, Frederick, Christina
Institution: New Jersey Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7206207958