Phase and Norm Retrieval via Projections in 2-Inner Product Spaces

Alshabhi, Salah H.

doi:10.28924/2291-8639-24-2026-44

Research Article

Phase and Norm Retrieval via Projections in 2-Inner Product Spaces

Salah H. Alshabhi

Abstract

This paper introduces and studies 2-phase retrieval and 2-norm retrieval in the context of 2-inner product spaces, generalizing classical phase and norm retrieval problems to a nonlinear geometric setting. A collection of subspaces \(\{W_i\}_{i=1}^M\) in a 2-inner product space \(V\) is said to yield {2-phase retrieval} if the 2-norms of projections \(\|P_i s\|_z = \|P_i b\|_z\) for all \(i\) and all reference vectors \(z \in V \setminus \{0\}\) imply that \(s\) and \(b\) are phase-equivalent (i.e., \(s = c b\) for some scalar \(c\) with \(|c| = 1\)). Similarly, \(\{W_i\}_{i=1}^M\) achieves 2-norm retrieval if the 2-norms \(\|P_i s\|_z\) uniquely determine the 2-norm \(\|s\|_z\) for all \(s \in V\) and all \(z\).

How to Cite

S. H. Alshabhi, Phase and Norm Retrieval via Projections in 2-Inner Product Spaces, Int. J. Anal. Appl. 24 (2026), 44. https://doi.org/10.28924/2291-8639-24-2026-44

BibTeX

@article{Alshabhi2026,
  author  = {Alshabhi, Salah H.},
  title   = {Phase and Norm Retrieval via Projections in 2-Inner Product Spaces},
  journal = {Int. J. Anal. Appl.},
  volume  = {24},
  year    = {2026},
  pages   = {44},
  doi     = {10.28924/2291-8639-24-2026-44}
}

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