On phase and norm retrieval by subspaces
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914232818204672 |
|---|---|
| author | Tran, Tin T. Huynh, Phung T. |
| author_facet | Tran, Tin T. Huynh, Phung T. |
| contents | This paper studies phase and norm retrieval by subspaces. We first investigate norm retrieval by hyperplanes. We show that if $N$ hyperplanes $\{φ_i^\perp\}_{i=1}^N\subset \mathbb{R}^N$ allow norm retrieval and the vectors $\{φ_i\}_{i=1}^N$ are linearly independent, then these vectors must be an orthonormal basis for $\mathbb{R}^N$. We then present several new properties of subspaces that allow phase and norm retrieval. In particular, we provide a complete classification of two proper subspaces that perform norm retrieval. It is known that the collection of norm-retrievable frames $\{φ_i\}_{i=1}^M$ in $\mathbb{R}^N$ is not dense in the set of all $M$-element frames when $M < 2N-1$. We extend this result to subspaces. Several alternative proofs of fundamental results in phase and norm retrieval are also provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01111 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On phase and norm retrieval by subspaces Tran, Tin T. Huynh, Phung T. Functional Analysis 42C15 This paper studies phase and norm retrieval by subspaces. We first investigate norm retrieval by hyperplanes. We show that if $N$ hyperplanes $\{φ_i^\perp\}_{i=1}^N\subset \mathbb{R}^N$ allow norm retrieval and the vectors $\{φ_i\}_{i=1}^N$ are linearly independent, then these vectors must be an orthonormal basis for $\mathbb{R}^N$. We then present several new properties of subspaces that allow phase and norm retrieval. In particular, we provide a complete classification of two proper subspaces that perform norm retrieval. It is known that the collection of norm-retrievable frames $\{φ_i\}_{i=1}^M$ in $\mathbb{R}^N$ is not dense in the set of all $M$-element frames when $M < 2N-1$. We extend this result to subspaces. Several alternative proofs of fundamental results in phase and norm retrieval are also provided. |
| title | On phase and norm retrieval by subspaces |
| topic | Functional Analysis 42C15 |
| url | https://arxiv.org/abs/2601.01111 |