LCA群上非负正定函数的积分比较
Integral comparisons of nonnegative positive definite functions on LCA groups
摘要：
在本文中，我们调查以下问题。设$μ, ν$是两个有限全变差的正则Borel测度.当$f$是一个连续非负正定函数时，我们什么时候有一个常数$C$满足$$\int f dν\le C \int f dμ$$？如何表征容许常数$C$，它们的最优值是什么？我们首先讨论局部紧阿贝尔群中的问题。然后，我们进一步的专业化时，Borel措施$μ, ν$都是纯原子或绝对连续的参考Haar措施。此外，我们证明了在我们的前一篇文章中提出的一个对偶猜想。
英文摘要：
In this paper we investigate the following questions. Let $μ, ν$ be two regular Borel measures of finite total variation. When do we have a constant $C$ satisfying $$\int f dν\le C \int f dμ$$ whenever $f$ is a continuous nonnegative positive definite function? How the admissible constants $C$ can be characterized, and what is their optimal value? We first discuss the problem in locally compact abelian groups. Then we make further specializations when the Borel measures $μ, ν$ are both either purely atomic or absolutely continuous with respect to a reference Haar measure. In addition, we prove a duality conjecture posed in our former paper.
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。
