Year: 2026
Type: article
Abstract: Let be a locally compact group. If is finite, then the amenability constant of its Fourier algebra, denoted by , admits an explicit formula [Johnson, J. Lond. Math. Soc. 1994]; if is infinite, then no such formula for is known, although lower and upper bounds were established by Runde [Proc. Am. Math. Soc. 2006]. Using non‐abelian Fourier analysis, we obtain a sharper upper bound for when is discrete. Combining this with previous work of the first author [Choi, Int. Math. Res. Not. 2023], we exhibit new examples of discrete groups and compact groups where 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.
DOI: 10.1112/jlms.70518
Authors: Y. Choi, M. Ghandehari
Institutions: Lancaster University, University of Delaware
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415971852