论文标题
傅立叶代数的舒适性常数的明确少数人
An explicit minorant for the amenability constant of the Fourier algebra
论文作者
论文摘要
我们表明，如果本地紧凑的$ g $是非亚洲的，那么其傅立叶代数的舒适性常数为$ \ geq 3/2 $，这扩展了约翰逊（JLMS，1994年）的结果，证明这是有限的非阿贝尔群体。我们的下限是最好的，这是以前的作者的结果，并回答了Runde提出的一个问题（Pams，2006年）。 为此，我们研究了与$ g \ times g $中的反对基因有关的少数人，该反对性是在runde的工作中隐含地使用的，但迄今未深入研究。就$ g $而言，当$ g $是一个几乎可数的阿贝利安集团时，我们的主要新颖性是这个少数人的明确公式。作为进一步的应用，我们表征了少数人达到其最低价值的那些非亚洲群体，并提出了一些示例，以支持少数人始终与不良性常数相吻合的猜想。
We show that if a locally compact group $G$ is non-abelian then the amenability constant of its Fourier algebra is $\geq 3/2$, extending a result of Johnson (JLMS, 1994) who proved that this holds for finite non-abelian groups. Our lower bound, which is known to be best possible, improves on results by previous authors and answers a question raised by Runde (PAMS, 2006). To do this we study a minorant for the amenability constant, related to the anti-diagonal in $G\times G$, which was implicitly used in Runde's work but hitherto not studied in depth. Our main novelty is an explicit formula for this minorant when $G$ is a countable virtually abelian group, in terms of the Plancherel measure for $G$. As further applications, we characterize those non-abelian groups where the minorant attains its minimal value, and present some examples to support the conjecture that the minorant always coincides with the amenability constant.
