B-Frames, B-Riesz bases, and Their tensor products
Abstract
Like g-frames, b-frames were introduced to generalize the concept of frames, allowing for broader applications in signal processing and other fields. The advantage of b-frames resides in their simpler definition, which may lead to reduced processing times. In this paper, we define dual b-frames and b-Riesz bases which were not precisely defined in previous literature and provide several characterizations of b-Riesz bases. We prove that the tensor product of two sequences, each lying in a Hilbert space, constitutes a b-frame (or a b-Riesz basis) if and only if both components of the product are b-frames (or b-Riesz bases). Finally, we establish a correspondence between b-frames and g-frames and propose a process for constructing frames induced by b-frames.
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BibTeX
@misc{bourouihiya2026bframes,
title = {{B-Frames, B-Riesz bases, and Their tensor products}},
author = {Abdelkrim Bourouihiya and Chaimae Mezzat},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.30967},
eprint = {2608.30967},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30967},
}
RIS
TY - UNPB
TI - B-Frames, B-Riesz bases, and Their tensor products
AU - Abdelkrim Bourouihiya
AU - Chaimae Mezzat
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2608.30967
UR - https://arxiv.org/abs/2608.30967
AB - Like g-frames, b-frames were introduced to generalize the concept of frames, allowing for broader applications in signal processing and other fields. The advantage of b-frames resides in their simpler definition, which may lead to reduced processing times. In this paper, we define dual b-frames and b-Riesz bases which were not precisely defined in previous literature and provide several characterizations of b-Riesz bases. We prove that the tensor product of two sequences, each lying in a Hilbert space, constitutes a b-frame (or a b-Riesz basis) if and only if both components of the product are b-frames (or b-Riesz bases). Finally, we establish a correspondence between b-frames and g-frames and propose a process for constructing frames induced by b-frames.
ER -