PreprintCC0arXiv
Irregular Gabor Frames for the Poisson Kernel
Abstract
Consider the semi-regular system of time-frequency shifts of the Poisson kernel g(t) = 1 over t2+w2 G(g, M × αZ) = { e2πi λt g(t−n) : (λ, n) ∈ M × αZ } where M ⊂ R. We obtain {\it a criterion} for G(g, M × αZ) to form a frame in L2(R) for an {\it arbitrary} set M of finite upper density. It turned out that the lower density alone does not determine the frame property, even when M is uniformly discrete.
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BibTeX
@misc{belov2026irregular,
title = {{Irregular Gabor Frames for the Poisson Kernel}},
author = {Yurii Belov and Andrei V. Semenov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30037},
eprint = {2610.30037},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30037},
note = {CC0},
}
RIS
TY - UNPB
TI - Irregular Gabor Frames for the Poisson Kernel
AU - Yurii Belov
AU - Andrei V. Semenov
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30037
UR - https://arxiv.org/abs/2610.30037
AB - Consider the semi-regular system of time-frequency shifts of the Poisson kernel g(t) = 1 over t^2+w^2 G(g, M × αZ) = { e^2πi λt g(t−n) : (λ, n) ∈ M × αZ } where M ⊂ R. We obtain {\it a criterion} for G(g, M × αZ) to form a frame in L^2(R) for an {\it arbitrary} set M of finite upper density. It turned out that the lower density alone does not determine the frame property, even when M is uniformly discrete.
ER -