关于Delsarte极值问题极值函数的存在性
On the Existence of an Extremal Function for the Delsarte Extremal Problem
AI总结：
本文研究局部紧阿贝尔群上Delsarte极值问题，证明当约束集Ω为闭集时极值函数存在，推广了先前已知的存在性结果。
摘要：
在局部紧阿贝尔群$G$的一般框架下，Delsarte极值问题要求计算连续正定函数$f: G \to \mathbb{R}$的积分上确界，这些函数满足$f(0) = 1$且其正部支集$\mathrm{supp} f_{+} \subset Ω$，其中$Ω$是某个有限测度的可测子集。本文考虑Delsarte极值问题极值函数的存在性问题。特别地，我们证明当$Ω$为闭集时，Delsarte问题存在极值函数，从而将先前已知的存在性结果推广到更大的一类函数。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
