On the inclusion relations between Gelfand-Shilov spaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911191340679168 |
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| author | Debrouwere, Andreas Neyt, Lenny Vindas, Jasson |
| author_facet | Debrouwere, Andreas Neyt, Lenny Vindas, Jasson |
| contents | We study inclusion relations between Gelfand-Shilov type spaces defined via a weight (multi-)sequence system, a weight function system, and a translation-invariant Banach function space. We characterize when such spaces are included into one another in terms of growth relations for the defining weight sequence and function systems. Our general framework allows for a unified treatment of the Gelfand-Shilov spaces $\mathcal{S}^{[M]}_{[A]}$ (defined via weight sequences $M$ and $A$) and the Beurling-Björck spaces $\mathcal{S}^{[ω]}_{[η]}$ (defined via weight functions $ω$ and $η$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06126 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the inclusion relations between Gelfand-Shilov spaces Debrouwere, Andreas Neyt, Lenny Vindas, Jasson Functional Analysis 46E10, 26E10 We study inclusion relations between Gelfand-Shilov type spaces defined via a weight (multi-)sequence system, a weight function system, and a translation-invariant Banach function space. We characterize when such spaces are included into one another in terms of growth relations for the defining weight sequence and function systems. Our general framework allows for a unified treatment of the Gelfand-Shilov spaces $\mathcal{S}^{[M]}_{[A]}$ (defined via weight sequences $M$ and $A$) and the Beurling-Björck spaces $\mathcal{S}^{[ω]}_{[η]}$ (defined via weight functions $ω$ and $η$). |
| title | On the inclusion relations between Gelfand-Shilov spaces |
| topic | Functional Analysis 46E10, 26E10 |
| url | https://arxiv.org/abs/2407.06126 |