PreprintarXiv licencearXiv
The zero set of the Zak transform of B-splines with applications to Gabor frames
Abstract
We study the zero sets of the Zak transform ZλBn(x,ν) of B-splines for λ> 0. Specifically, we provide a full characterization of the zero set for the hat spline for all positive values of the parameter λ and for higher order B-splines when λ> 1. Finally, we apply these results to establish the frame property of integer-oversampled Gabor systems generated by B-splines. In particular, we characterize the frame property for integer-oversampled Gabor systems generated by the hat splines.
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BibTeX
@misc{hasannasab2026zero,
title = {{The zero set of the Zak transform of B-splines with applications to Gabor frames}},
author = {Marzieh Hasannasab and Jakob Lemvig},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13116},
eprint = {2609.13116},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13116},
}
RIS
TY - UNPB
TI - The zero set of the Zak transform of B-splines with applications to Gabor frames
AU - Marzieh Hasannasab
AU - Jakob Lemvig
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.13116
UR - https://arxiv.org/abs/2609.13116
AB - We study the zero sets of the Zak transform Z_λB_n(x,ν) of B-splines for λ> 0. Specifically, we provide a full characterization of the zero set for the hat spline for all positive values of the parameter λ and for higher order B-splines when λ> 1. Finally, we apply these results to establish the frame property of integer-oversampled Gabor systems generated by B-splines. In particular, we characterize the frame property for integer-oversampled Gabor systems generated by the hat splines.
ER -