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

Erik Bedos; Roberto Conti

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

Erik Bedos·Roberto Conti

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Abstract

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.

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BibTeX RIS

Erik Bedos, Roberto Conti. 2008-02-21. On twisted Fourier analysis and convergence of Fourier series on discrete groups. https://arxiv.org/abs/math/0605145

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