2025/07/07 by Choi, Yemon, Ghandehari, Mahya
#20C15 #22D10 (secondary) #43A30 #46H20 (primary) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2507.05243
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.