On some properties of modulation spaces as Banach algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910448132030464 |
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| author | Feichtinger, Hans G. Kobayashi, Masaharu Sato, Enji |
| author_facet | Feichtinger, Hans G. Kobayashi, Masaharu Sato, Enji |
| contents | In this paper, we give some properties of the modulation spaces $M_s^{p,1}({\mathbf R}^n)$ as commutative Banach algebras. In particular, we show the Wiener-Lévy theorem for $M^{p,1}_s({\mathbf R}^n)$, and clarify the sets of spectral synthesis for $M^{p,1}_s ({\mathbf R}^n)$ by using the ``ideal theory for Segal algebras'' developed in Reiter [30].The inclusion relationship between the modulation space $M^{p,1}_0 ({\mathbf R})$ and the Fourier Segal algebra ${\mathcal F}\hspace{-0.08cm}A_p({\mathbf R})$ is also determined. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09058 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On some properties of modulation spaces as Banach algebras Feichtinger, Hans G. Kobayashi, Masaharu Sato, Enji Functional Analysis In this paper, we give some properties of the modulation spaces $M_s^{p,1}({\mathbf R}^n)$ as commutative Banach algebras. In particular, we show the Wiener-Lévy theorem for $M^{p,1}_s({\mathbf R}^n)$, and clarify the sets of spectral synthesis for $M^{p,1}_s ({\mathbf R}^n)$ by using the ``ideal theory for Segal algebras'' developed in Reiter [30].The inclusion relationship between the modulation space $M^{p,1}_0 ({\mathbf R})$ and the Fourier Segal algebra ${\mathcal F}\hspace{-0.08cm}A_p({\mathbf R})$ is also determined. |
| title | On some properties of modulation spaces as Banach algebras |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2405.09058 |