8 papers · 1 filter
Discrete Quaternionic (Multi-window) Gabor Systems
Najib Khachiaa
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 , and defined by:…
Results on Continuous -frames for Quaternionic (Super) Hilbert Spaces
Najib Khachiaa
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 \( \…
On -frames for Quaternionic Hilbert Spaces
Najib Khachiaa
The aim of this paper is to study -frames for quaternionic Hilbert spaces. First, we present the quaternionic version of Douglas's theorem and then investigate -frames for a…
Frames and Operators on Quaternionic Hilbert spaces
Najib Khachiaa
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…
Admissibility of Multi-window Gabor Systems in Periodically Supported -spaces with Vector-valued Sequences
Najib Khachiaa
In this paper, \( L, M, N, R \) are positive integers, and \( \mathbb{S} \) is an \( N \)-periodic subset of \( \mathbb{Z} \). The space \( \ell^2(\mathbb{S}, \mathbb{C}^R) \) deno…
Discrete Zak Transform and Multi-window Gabor Systems on Discrete Periodic Sets
Najib Khachiaa
In this paper, denotes a window Gabor system on a periodic set , where and $g=\{g_l\}_{l\in \mathbb{N}_L}\subset \ell^2…
Multi-window Gabor systems on discrete periodic sets
Najib Khachiaa
In this paper, we study multiwindow discrete Gabor systems on discrete periodic sets and give some necessary and/or sufficient matrix-…
frames for Super Hilbert Spaces
Najib Khachiaa
Let and be two Hilbert spaces, and be bounded operatrors on and respectively. In this paper we study the relationship between -frames for a…