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Quaternionic Gabor frame characterization and the density theorem
The study of quaternionic Gabor systems has interested some mathematicians in recent years. From the literature, we found that most existing results...
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Dilations of fusion frame generators for Gabor type unitary systems
Wandering subspaces are closely related with wavelets. Fusion frames are a generalization of frames in Hilbert spaces that is more acceptable to...
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On Riesz duals for Gabor systems on LCA groups
In the context of separable uniform time-frequency lattices in locally compact abelian groups, we analyse the circumstances in which, for a given...
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A Note on the Invertibility of the Gabor Frame Operator on Certain Modulation Spaces
We consider Gabor frames generated by a general lattice and a window function that belongs to one of the following spaces: the Sobolev space
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Discrete Gabor frames and K-discrete Gabor frames
The theory of discrete Gabor (D-G) frames has attracted many mathematicians and engineers due to its potential applications in digital signal...
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Star DGT: a robust Gabor transform for speech denoising
In this paper, we address the speech denoising problem, where Gaussian and coloured additive noises are to be removed from a given speech signal. Our...
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Cohn–Elkies Functions from Gabor Frames
We investigate the relation between two different mathematical problems: the construction of bounds on sphere packing density using Cohn–Elkies...
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Measure-operator convolutions and applications to mixed-state Gabor multipliers
For the Weyl-Heisenberg group, convolutions between functions and operators were defined by Werner as a part of a framework called quantum harmonic...
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Characterization of Schauder basis property of Gabor systems in local fields
Let K be a totally disconnected, locally compact and nondiscrete field of positive characteristic and D be its ring of integers. We characterize the...
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On the relation of the frame-related operators of fusion frame systems
Frames have been investigated frequently over the last few decades due to their valuable properties, which are desirable for various applications as...
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Translation partitions of unity, symmetry properties, and Gabor frames
We consider the general question of constructing a partition of unity formed by translates of a compactly supported function g : ℝ d → ℂ. In...
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Gabor Neural Networks with Proven Approximation Properties
In this paper, we propose a new type of a neural network which is inspired by Gabor systems from harmonic analysis. In this regard, we construct a...
