Constructing Parseval Fusion Frames via Operators
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912615242924032 |
|---|---|
| author | Ameli, Ehsan Arefijamaal, Ali Akbar Neyshaburi, Fahimeh Arabyani |
| author_facet | Ameli, Ehsan Arefijamaal, Ali Akbar Neyshaburi, Fahimeh Arabyani |
| contents | This article explores the problem of modifying the subspaces of a fusion frame in order to construct a Parseval fusion frame. In this respect, the notion of scalability is extended to the fusion frame setting. Then, scalable fusion Riesz bases are characterized, and a concrete form for scalable 1-excess fusion frames is obtained. Furthermore, it is shown that 1-excess dual fusion frames of a fusion Riesz basis are not scalable. Finally, several examples are exhibited to confirm the acquired results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25108 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constructing Parseval Fusion Frames via Operators Ameli, Ehsan Arefijamaal, Ali Akbar Neyshaburi, Fahimeh Arabyani Functional Analysis Primary 42C15, Secondary 15A12 This article explores the problem of modifying the subspaces of a fusion frame in order to construct a Parseval fusion frame. In this respect, the notion of scalability is extended to the fusion frame setting. Then, scalable fusion Riesz bases are characterized, and a concrete form for scalable 1-excess fusion frames is obtained. Furthermore, it is shown that 1-excess dual fusion frames of a fusion Riesz basis are not scalable. Finally, several examples are exhibited to confirm the acquired results. |
| title | Constructing Parseval Fusion Frames via Operators |
| topic | Functional Analysis Primary 42C15, Secondary 15A12 |
| url | https://arxiv.org/abs/2509.25108 |