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arXiv · 2503.14249

About an isomorphism between the Beurling algebra with a weight dependent convolution and the $L^1(G)$ group algebra

Raúl Rodríguez-Barrera·Francisco Torres-Ayala
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Abstract

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 $\mathscr{L}^1(G,\omega)$ 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.

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Raúl Rodríguez-Barrera, Francisco Torres-Ayala. 2025-03-18. About an isomorphism between the Beurling algebra with a weight dependent convolution and the $L^1(G)$ group algebra. https://arxiv.org/abs/2503.14249

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