On the Existence of an Extremal Function for the Delsarte Extremal Problem
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909402202636288 |
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| author | Ramabulana, Mita Dimpho |
| author_facet | Ramabulana, Mita Dimpho |
| contents | In the general setting of a locally compact Abelian group $G$, the Delsarte extremal problem asks for the supremum of integrals over the collection of continuous positive definite functions $f: G \to \mathbb{R}$ satisfying $f(0) = 1$ and having $\mathrm{supp} f_{+} \subset Ω$ for some measurable subset $Ω$ of finite measure. In this paper, we consider the question of the existence of an extremal function for the Delsarte extremal problem. In particular, we show that there exists an extremal function for the Delsarte problem when $Ω$ is closed, extending previously known existence results to a larger class of functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04410 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Existence of an Extremal Function for the Delsarte Extremal Problem Ramabulana, Mita Dimpho Classical Analysis and ODEs Functional Analysis 43A35 In the general setting of a locally compact Abelian group $G$, the Delsarte extremal problem asks for the supremum of integrals over the collection of continuous positive definite functions $f: G \to \mathbb{R}$ satisfying $f(0) = 1$ and having $\mathrm{supp} f_{+} \subset Ω$ for some measurable subset $Ω$ of finite measure. In this paper, we consider the question of the existence of an extremal function for the Delsarte extremal problem. In particular, we show that there exists an extremal function for the Delsarte problem when $Ω$ is closed, extending previously known existence results to a larger class of functions. |
| title | On the Existence of an Extremal Function for the Delsarte Extremal Problem |
| topic | Classical Analysis and ODEs Functional Analysis 43A35 |
| url | https://arxiv.org/abs/2407.04410 |