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The main purpose of the paper is to give a characterization of all compactly supported dual windows of a Gabor frame. As an application, we consider an iterative procedure for approximation of the canonical dual window via compactly supported dual windows on every step. In particular, the procedure allows to have approximation of the canonical dual window via dual windows from certain modulation spaces or from the Schwartz space.
In the past decade, significant progress has been made to generalize classical tools from Fourier analysis to analyze and process signals defined on networks. In this paper, we propose a new framework for constructing Gabor-type frames for signals on
Given a locally compact abelian group $G$ and a closed subgroup $Lambda$ in $Gtimeswidehat{G}$, Rieffel associated to $Lambda$ a Hilbert $C^*$-module $mathcal{E}$, known as a Heisenberg module. He proved that $mathcal{E}$ is an equivalence bimodule b
This paper is a contribution to frame theory. Frames in a Hilbert space are generalizations of orthonormal bases. In particular, Gabor frames of $L^2(mathbb{R})$, which are made of translations and modulations of one or more windows, are often used i
We generalize Feichtinger and Kaiblingers theorem on linear deformations of uniform Gabor frames to the setting of a locally compact abelian group $G$. More precisely, we show that Gabor frames over lattices in the time-frequency plane of $G$ with wi
A dual frames multiplier is an operator consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames in a Hilbert space, respectively. In this paper we investigate the spectra of som