On twisted Fourier analysis and convergence of Fourier series on discrete groups

Title: On twisted Fourier analysis and convergence of Fourier series on discrete groups
Creator: Bédos, Erik; Conti, Roberto
Relation: Journal of Fourier Analysis and Applications Vol. 15, Issue 3, p. 336-365
Publisher Link: http://dx.doi.org/10.1007/s00041-009-9067-z
Publisher: Springer
Resource Type: journal article
Date: 2009
Description: 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.
Subject: twisted group C*-algebra; Fourier series; Fejér summation; Abel-Poisson summation; amenable group; Haagerup property; length function; polynomial growth; subexponential growth
Identifier: uon:7693
Identifier: http://hdl.handle.net/1959.13/808580
Identifier: ISSN:1069-5869
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