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May 17, 2026International Journal of Wavelets Multiresolution and Information Processing0 citations

2-frames and 2-Riesz bases associated with Hilbert spaces

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YLYun-Zhang LiYLYu-He Liu

Key Points

  • This research aims to explore the connections among frames, Riesz bases, 2-frames, and 2-Riesz bases in Hilbert spaces.
  • Developed the concept of a 2-inner product based on a Hilbert space inner product.
  • Established links among frames, Riesz bases, 2-frames, and 2-Riesz bases.
  • Investigated the existence and characterizations of 2-Riesz bases.
  • Identified relationships between conventional frames and their 2-dimensional analogs.
  • Characterized conditions under which 2-Riesz bases exist.
  • Provided new insights into the structure of 2-frames within Hilbert spaces.

Abstract

This paper addresses 2-frames and 2-Riesz bases based on a 2-inner product induced by a Hilbert space inner product. We establish some links among frames, Riesz bases, 2-frames and 2-Riesz bases; and investigate the existence and characterizations of 2-Riesz bases.

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Cite This Study

Li et al. (2026) studied this question.

synapsesocial.com/papers/6a095bdd7880e6d24efe1c55https://doi.org/10.1142/s0219691326500177
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