Salvato in:
| Autori principali: | , , , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2303.01202 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929412118675456 |
|---|---|
| author | Köhldorfer, Lukas Balazs, Peter Casazza, Pete Heineken, Sigrid Hollomey, Clara Morillas, Patricia Shamsabadi, Mitra |
| author_facet | Köhldorfer, Lukas Balazs, Peter Casazza, Pete Heineken, Sigrid Hollomey, Clara Morillas, Patricia Shamsabadi, Mitra |
| contents | Fusion frames are a very active area of research today because of their myriad of applications in pure mathematics, applied mathematics, engineering, medicine, signal and image processing and much more. They provide a great flexibility for designing sets of vectors for applications and are therefore prominent in all these areas, including e.g. mitigating the effects of noise in a signal or giving robustness to erasures. In this chapter, we present the fundamentals of fusion frame theory with an emphasis on their delicate relation to frame theory. The goal here is to provide researchers and students with an easy entry into this topic. Proofs for fusion frames will be self-contained and differences between frames and fusion frames are analyzed. In particular, we focus on the subtleties of fusion frame duality. We also provide a reproducible research implementation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_01202 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Survey of Fusion Frames in Hilbert Spaces Köhldorfer, Lukas Balazs, Peter Casazza, Pete Heineken, Sigrid Hollomey, Clara Morillas, Patricia Shamsabadi, Mitra Functional Analysis Fusion frames are a very active area of research today because of their myriad of applications in pure mathematics, applied mathematics, engineering, medicine, signal and image processing and much more. They provide a great flexibility for designing sets of vectors for applications and are therefore prominent in all these areas, including e.g. mitigating the effects of noise in a signal or giving robustness to erasures. In this chapter, we present the fundamentals of fusion frame theory with an emphasis on their delicate relation to frame theory. The goal here is to provide researchers and students with an easy entry into this topic. Proofs for fusion frames will be self-contained and differences between frames and fusion frames are analyzed. In particular, we focus on the subtleties of fusion frame duality. We also provide a reproducible research implementation. |
| title | A Survey of Fusion Frames in Hilbert Spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2303.01202 |