2019/01/04 by Markus Faulhuber, Faulhuber, Markus
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1901.01220
openalex publication_date 2019/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we show that if the frame property of a Gabor frame with window\nin Feichtinger's algebra and a fixed lattice only depends on the parity of the\nwindow, then the lattice can be replaced by any other lattice of the same\ndensity without losing the frame property. As a byproduct we derive a\ngeneralization of a result of Lyubarskii and Nes, who could show that any Gabor\nsystem consisting of an odd window function from Feichtinger's algebra and any\nseparable lattice of density \(n+1)/(n), n \∈ \ℕ+, cannot be a\nGabor frame for the Hilbert space of square-integrable functions on the real\nline. We extend this result by removing the assumption that the lattice has to\nbe separable. This is achieved by exploiting the interplay between the\nsymplectic and the metaplectic group.\n