Restriction theorems for the $p$-analog of the Fourier-Stieltjes algebra
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913359708815360 |
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| author | Dabra, Arvish Kumar, N. Shravan |
| author_facet | Dabra, Arvish Kumar, N. Shravan |
| contents | For a locally compact group $G$ and $1 < p < \infty,$ let $B_p(G)$ denote the $p$-analog of the Fourier-Stieltjes algebra $B(G) \, (\text{or} \, B_2(G))$. Let $r: B_p(G) \to B_p(H)$ be the restriction map given by $r(u) = u|_H$ for any closed subgroup $H$ of $G.$ In this article, we prove that the restriction map $r$ is a surjective isometry for any open subgroup $H$ of $G.$ Further, we show that the range of the map $r$ is dense in $B_p(H)$ when $H$ is either a compact normal subgroup of $G$ or compact subgroup of an [SIN]$_H$-group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14227 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Restriction theorems for the $p$-analog of the Fourier-Stieltjes algebra Dabra, Arvish Kumar, N. Shravan Functional Analysis Primary 43A15, 43A25, 46J10, Secondary 22D12, 43A65 For a locally compact group $G$ and $1 < p < \infty,$ let $B_p(G)$ denote the $p$-analog of the Fourier-Stieltjes algebra $B(G) \, (\text{or} \, B_2(G))$. Let $r: B_p(G) \to B_p(H)$ be the restriction map given by $r(u) = u|_H$ for any closed subgroup $H$ of $G.$ In this article, we prove that the restriction map $r$ is a surjective isometry for any open subgroup $H$ of $G.$ Further, we show that the range of the map $r$ is dense in $B_p(H)$ when $H$ is either a compact normal subgroup of $G$ or compact subgroup of an [SIN]$_H$-group. |
| title | Restriction theorems for the $p$-analog of the Fourier-Stieltjes algebra |
| topic | Functional Analysis Primary 43A15, 43A25, 46J10, Secondary 22D12, 43A65 |
| url | https://arxiv.org/abs/2405.14227 |