Sequence space representations of Beurling-Björck spaces via Gabor frames and Wilson bases
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916885376794624 |
|---|---|
| author | Debrouwere, Andreas Neyt, Lenny |
| author_facet | Debrouwere, Andreas Neyt, Lenny |
| contents | We establish sequence space representations of a broad class of Beurling-Björck spaces $\mathcal{S}^{(ω)}_{(η)}$ and $\mathcal{S}^{\{ω\}}_{\{η\}}$. We develop two different approaches: a non-constructive one based on Gabor frames and the structure theory of Fréchet spaces, and a constructive one using Wilson bases, under stronger assumptions on the defining weight functions $ω$ and $η$. As an application, we provide an isomorphic classification of the spaces $\mathcal{S}^{(ω)}_{(η)}$ and $\mathcal{S}^{\{ω\}}_{\{η\}}$ in terms of $ω$ and $η$. In particular, our results are applicable to the classical Gelfand-Shilov spaces $\mathcal{S}^μ_τ$ for $μ, τ\geq 1/2$ (non-constructive approach) and $μ, τ\geq 1$ (constructive approach). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05565 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sequence space representations of Beurling-Björck spaces via Gabor frames and Wilson bases Debrouwere, Andreas Neyt, Lenny Functional Analysis Primary. 46A45, 46E10, 46F05. Secondary. 42B10, 81S30 We establish sequence space representations of a broad class of Beurling-Björck spaces $\mathcal{S}^{(ω)}_{(η)}$ and $\mathcal{S}^{\{ω\}}_{\{η\}}$. We develop two different approaches: a non-constructive one based on Gabor frames and the structure theory of Fréchet spaces, and a constructive one using Wilson bases, under stronger assumptions on the defining weight functions $ω$ and $η$. As an application, we provide an isomorphic classification of the spaces $\mathcal{S}^{(ω)}_{(η)}$ and $\mathcal{S}^{\{ω\}}_{\{η\}}$ in terms of $ω$ and $η$. In particular, our results are applicable to the classical Gelfand-Shilov spaces $\mathcal{S}^μ_τ$ for $μ, τ\geq 1/2$ (non-constructive approach) and $μ, τ\geq 1$ (constructive approach). |
| title | Sequence space representations of Beurling-Björck spaces via Gabor frames and Wilson bases |
| topic | Functional Analysis Primary. 46A45, 46E10, 46F05. Secondary. 42B10, 81S30 |
| url | https://arxiv.org/abs/2508.05565 |