Publisher Correction: Quaternionic Gabor frame characterization and the density theorem
نویسندگان
چکیده
منابع مشابه
Relaxed quaternionic Gabor expansions at critical density
Shifted and modulated Gaussian functions play a vital role in the representation of signals. We extend the theory into a quaternionic setting, using two exponential kernels with two complex numbers. As a final result, we show that every continuous and quaternion-valued signal f in the Wiener space can be expanded into a unique `2 series on a lattice at critical density 1, provided one more poin...
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Let A ⊂ L2(R) be at most countable, and p, q ∈ N. We characterize various frame-properties for Gabor systems of the form G(1, p/q,A)= {e2 g(x − np/q) : m, n ∈ Z, g ∈ A} in terms of the corresponding frame properties for the row vectors in the Zibulski–Zeevi matrix. This extends work by [Ron and Shen, Weyl–Heisenberg systems and Riesz bases in L2(R d). Duke Math. J. 89 (1997) 237–282], who consi...
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ژورنال
عنوان ژورنال: Banach Journal of Mathematical Analysis
سال: 2023
ISSN: ['1735-8787', '2662-2033']
DOI: https://doi.org/10.1007/s43037-023-00298-7