Zobrazeno 1 - 10
of 185
pro vyhledávání: '"42C15, 42C40"'
Autor:
Khachiaa, Najib
The aim of this work is to study (Multi-window) Gabor systems in the space \(\ell^2(\mathbb{Z} \times \mathbb{Z}, \mathbb{H})\), denoted by $\mathcal{G}(g,L,M,N)$, and defined by: \[ \left\{ (k_1,k_2)\in \mathbb{Z}^2\mapsto e^{2\pi i \frac{m_1}{M}k_1
Externí odkaz:
http://arxiv.org/abs/2411.16988
Autor:
Khachiaa, Najib
This paper aims to explore the concept of continuous \( K \)-frames in quaternionic Hilbert spaces. First, we investigate \( K \)-frames in a single quaternionic Hilbert space \( \mathcal{H} \), where \( K \) is a right $\mathbb{H}$-linear bounded op
Externí odkaz:
http://arxiv.org/abs/2411.07937
Autor:
Khachiaa, Najib
The aim of this paper is to study $K$-frames for quaternionic Hilbert spaces. First, we present the quaternionic version of Douglas's theorem and then investigate $K$-frames for a quaternionic Hilbert space $\mathcal{H}$, where $K \in \mathbb{B}(\mat
Externí odkaz:
http://arxiv.org/abs/2411.04154
Autor:
Khachiaa, Najib
The aim of this work is to study frame theory in quaternionic Hilbert spaces. We provide a characterization of frames in these spaces through the associated operators. Additionally, we examine frames of the form $\{Lu_i\}_{i \in I}$, where $L$ is a r
Externí odkaz:
http://arxiv.org/abs/2411.03790
Autor:
Khachiaa, Najib, Rossafi, Mohamed
In this paper, $\mathcal{G}(g,L,M,N)$ denotes a $L-$window Gabor system on a periodic set $\mathbb{S}$, where $L,M,M\in \mathbb{N}$ and $g=\{g_l\}_{l\in \mathbb{N}_L}\subset \ell^2(\mathbb{S})$. We characterize which $g$ generates a complete multi-wi
Externí odkaz:
http://arxiv.org/abs/2409.03423
Autor:
Gorsanova, Anastassia, Lebedeva, Elena
We provide constructive necessary and sufficient conditions for a family of periodic wavelets to be a Parseval wavelet frame. The criterion generalizes unitary and oblique extension principles. The case of one wavelet generator and refinable function
Externí odkaz:
http://arxiv.org/abs/2409.01165
Weak R-duals, a generalization of R-duals, were recently introduced; for which duality relations were established. In this paper, we consider the problem of characterizing a given frame sequence to be a weak R-dual of a given frame. Further, we apply
Externí odkaz:
http://arxiv.org/abs/2408.14952
In this paper, we study multiwindow discrete Gabor $(M-D-G)$ systems $\mathcal{G}(g,L,M,N)$ on discrete periodic sets $\mathbb{S}$ and give some necessary and/or sufficient matrix-conditions for a $M-D-G$ system in $\ell^2(\mathbb{S})$ to be a frame.
Externí odkaz:
http://arxiv.org/abs/2407.05495
Autor:
Deepshikha, Samanta, Aniruddha
Recently, the concept of frames generated by graphs has been introduced in \cite{D}. In this paper, we study spectrally optimal dual frames of frames generated by graphs. We show that if the frame is generated by a connected graph, then its canonical
Externí odkaz:
http://arxiv.org/abs/2406.00776
Autor:
Deepshikha, Samanta, Aniruddha
Erasures are a common problem that arises while signals or data are being transmitted. A profound challenge in frame theory is to find the optimal dual frames ($OD$-frames) to minimize the reconstruction error if erasures occur. In this paper, we stu
Externí odkaz:
http://arxiv.org/abs/2405.18189