A Survey on Constructing Parseval Fusion Frames via Scaling Weights
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917923194404864 |
|---|---|
| author | Ameli, Ehsan Arefijamaal, Ali Akbar Neyshaburi, Fahimeh Arabyani |
| author_facet | Ameli, Ehsan Arefijamaal, Ali Akbar Neyshaburi, Fahimeh Arabyani |
| contents | The construction of Parseval fusion frames is highly desirable in a wide range of signal processing applications. In this paper, we study the problem of modifying the weights of a fusion frame in order to generate a Parseval fusion frame. To this end, we extend the notion of the scalability to the fusion frame setting. We then proceed to characterize scalable fusion Riesz bases and $1$-excess fusion frames. Furthermore, we provide the necessary and sufficient conditions for the scalability of certain $k$-excess fusion frames, $k\geq 2$. Finally, we present several pertinent examples to confirm the obtained results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10244 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Survey on Constructing Parseval Fusion Frames via Scaling Weights Ameli, Ehsan Arefijamaal, Ali Akbar Neyshaburi, Fahimeh Arabyani Functional Analysis Primary 42C15, Secondary 15A12 The construction of Parseval fusion frames is highly desirable in a wide range of signal processing applications. In this paper, we study the problem of modifying the weights of a fusion frame in order to generate a Parseval fusion frame. To this end, we extend the notion of the scalability to the fusion frame setting. We then proceed to characterize scalable fusion Riesz bases and $1$-excess fusion frames. Furthermore, we provide the necessary and sufficient conditions for the scalability of certain $k$-excess fusion frames, $k\geq 2$. Finally, we present several pertinent examples to confirm the obtained results. |
| title | A Survey on Constructing Parseval Fusion Frames via Scaling Weights |
| topic | Functional Analysis Primary 42C15, Secondary 15A12 |
| url | https://arxiv.org/abs/2502.10244 |