发表机构
Nova Southeastern University; Faculty of Science, Ibn Tofail University（新东南大学; 伊本·图费利大学理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文定义了对偶b-框架和b-里斯基，证明了两序列的张量积为b-框架（或b-里斯基）的充要条件，建立了b-框架与g-框架的对应关系并提出了由b-框架诱导框架的构造方法。
AI 中文摘要
与g-框架类似，b-框架的提出是为了推广框架的概念，以在信号处理及其他领域获得更广泛的应用。b-框架的优势在于其定义更简单，这可能会缩短处理时间。本文定义了以往文献中未精确定义的对偶b-框架和b-里斯基，并给出了b-里斯基的若干刻画。我们证明：分别属于两个希尔伯特空间的两个序列的张量积构成b-框架（或b-里斯基）当且仅当该乘积的两个分量均为b-框架（或b-里斯基）。最后，我们建立了b-框架与g-框架之间的对应关系，并提出了由b-框架诱导框架的构造方法。
英文摘要
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.
