Connections between $\mathcal{S}$-operators and restriction estimates for spheres over finite fields
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915157207154688 |
|---|---|
| author | Kang, Hunseok Koh, Doowon |
| author_facet | Kang, Hunseok Koh, Doowon |
| contents | In this paper, we introduce a new operator, $\mathcal{S}$, which is closely related to the restriction problem for spheres in $\mathbb{F}_q^d$, the $d$-dimensional vector space over the finite field $\mathbb{F}_q$ with $q$ elements. The $\mathcal{S}$ operator is considered as a specific operator that maps functions on $\mathbb{F}_q^d$ to functions on $\mathbb{F}_q^{d+1}$. We explore a relationship between the boundedness of the $\mathcal{S}$ operator and the restriction estimate for spheres in $\mathbb{F}_q^d$. Consequently, using this relationship, we prove that the $L^2$ restriction conjectures for spheres hold in all dimensions when the test functions are restricted to homogeneous functions of degree zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12294 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Connections between $\mathcal{S}$-operators and restriction estimates for spheres over finite fields Kang, Hunseok Koh, Doowon Classical Analysis and ODEs Analysis of PDEs 42B05, 43A32, 43A15 In this paper, we introduce a new operator, $\mathcal{S}$, which is closely related to the restriction problem for spheres in $\mathbb{F}_q^d$, the $d$-dimensional vector space over the finite field $\mathbb{F}_q$ with $q$ elements. The $\mathcal{S}$ operator is considered as a specific operator that maps functions on $\mathbb{F}_q^d$ to functions on $\mathbb{F}_q^{d+1}$. We explore a relationship between the boundedness of the $\mathcal{S}$ operator and the restriction estimate for spheres in $\mathbb{F}_q^d$. Consequently, using this relationship, we prove that the $L^2$ restriction conjectures for spheres hold in all dimensions when the test functions are restricted to homogeneous functions of degree zero. |
| title | Connections between $\mathcal{S}$-operators and restriction estimates for spheres over finite fields |
| topic | Classical Analysis and ODEs Analysis of PDEs 42B05, 43A32, 43A15 |
| url | https://arxiv.org/abs/2502.12294 |