About an isomorphism between the Beurling algebra with a weight dependent convolution and the $L^1(G)$ group algebra
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915203683188736 |
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| author | Rodríguez-Barrera, Raúl Torres-Ayala, Francisco |
| author_facet | Rodríguez-Barrera, Raúl Torres-Ayala, Francisco |
| contents | We show that the Beurling algebra with a weight-dependent convolution and the group algebra $L^1(G)$ are isomorphic. In particular, using this isomorphism, we extend some results of the algebra $\mathscr{L}^1(G,ω)$ presented in recent articles. As a main result, we explicitly construct the equivalence between unitary representations of the group and non-degenerate $\ast$-representations of this algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14249 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | About an isomorphism between the Beurling algebra with a weight dependent convolution and the $L^1(G)$ group algebra Rodríguez-Barrera, Raúl Torres-Ayala, Francisco Functional Analysis We show that the Beurling algebra with a weight-dependent convolution and the group algebra $L^1(G)$ are isomorphic. In particular, using this isomorphism, we extend some results of the algebra $\mathscr{L}^1(G,ω)$ presented in recent articles. As a main result, we explicitly construct the equivalence between unitary representations of the group and non-degenerate $\ast$-representations of this algebra. |
| title | About an isomorphism between the Beurling algebra with a weight dependent convolution and the $L^1(G)$ group algebra |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2503.14249 |