On Twisted Fourier Analysis and Convergence of Fourier Series on Discrete Groups
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- Bédos, E. & Conti, R. J Fourier Anal Appl (2009) 15: 336. doi:10.1007/s00041-009-9067-z
We study norm convergence and summability of Fourier series in the setting of reduced twisted group C*-algebras of discrete groups. For amenable groups, Følner nets give the key to Fejér summation. We show that Abel-Poisson summation holds for a large class of groups, including e.g. all Coxeter groups and all Gromov hyperbolic groups. As a tool in our presentation, we introduce notions of polynomial and subexponential H-growth for countable groups w.r.t. proper scale functions, usually chosen as length functions. These coincide with the classical notions of growth in the case of amenable groups.