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arXiv · 2102.08901

Harmonic Analysis of Covariant Functions of Characters of Normal Subgroups

Arash Ghaani Farashahi
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Abstract

Let $G$ be a locally compact group with the group algebra $L^1(G)$ and $N$ be a closed normal subgroup of $G$. Suppose that $\xi:N\to\mathbb{T}$ is a continuous character and $L_\xi^1(G,N)$ is the $L^1$-space of all covariant functions of $\xi$ on $G$. We showed that $L^1_\xi(G,N)$ is isometrically isomorphic to a quotient space of $L^1(G)$. It is also proved that the dual space $L^1_\xi(G,N)^*$ is isometrically isomorphic to $L^\infty_\xi(G,N)$.

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Arash Ghaani Farashahi. 2021-02-17. Harmonic Analysis of Covariant Functions of Characters of Normal Subgroups. https://arxiv.org/abs/2102.08901

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