标题： 关于傅里叶代数的可约常数：新的界限和新的例子 显示英文标题

标题： On amenability constants of Fourier algebras: new bounds and new examples

摘要： 设$G$是一个局部紧致群。 如果$G$是有限的，那么其傅里叶代数的可均常数，记为${\rm AM}({\rm A}(G))$，有一个显式公式 [Johnson, JLMS 1994]；如果$G$是无限的，则目前尚不知道${\rm AM}({\rm A}(G))$的此类公式，尽管 Runde [PAMS 2006] 建立了下界和上界。 利用非交换傅里叶分析，我们得到当$G$是离散时，${\rm AM}({\rm A}(G))$的更紧的上界。 结合第一作者之前的的工作 [Choi, IMRN 2023]，我们展示了离散群和紧群的新例子，其中${\rm AM}({\rm A}(G))$可以显式计算；之前仅知道有限群与“退化”情况的乘积群有此性质。 我们的新例子也提供了额外的证据来支持 Runde 的可换常数下界实际上是一个等式的猜想。 显示英文摘要

摘要： Let $G$ be a locally compact group. If $G$ is finite then the amenability constant of its Fourier algebra, denoted by ${\rm AM}({\rm A}(G))$, admits an explicit formula [Johnson, JLMS 1994]; if $G$ is infinite then no such formula for ${\rm AM}({\rm A}(G))$ is known, although lower and upper bounds were established by Runde [PAMS 2006]. Using non-abelian Fourier analysis, we obtain a sharper upper bound for ${\rm AM}({\rm A}(G))$ when $G$ is discrete. Combining this with previous work of the first author [Choi, IMRN 2023], we exhibit new examples of discrete groups and compact groups where ${\rm AM}({\rm A}(G))$ can be calculated explicitly; previously this was only known for groups that are products of finite groups with ``degenerate'' cases. Our new examples also provide additional evidence to support the conjecture that Runde's lower bound for the amenability constant is in fact an equality.