The frameset of the second-order B-Spline along ab=1/q
Alexander Stangl, Christina Frederick
Abstract
We give a complete characterization of the zero set of the Zak transform of the second-order B-spline Q2. As a consequence, we obtain a new proof of the Lemvig--Nielsen obstructions to the Gabor frame property of Q2, 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 F(Q2) along an entire curve in this family, resolving a question left open by Lemvig and Nielsen.
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