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On Twisted Fourier Analysis and Convergence of Fourier Series on Discrete Groups

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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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  1. Roberto Conti

    Present address: Department of Mathematics, University of Rome 2 Tor Vergata, via della Ricerca Scientifica, 00133, Rome, Italy

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  1. Institute of Mathematics, University of Oslo, P.B. 1053 Blindern, 0316, Oslo, Norway

    Erik Bédos

  2. Mathematics, School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW, 2308, Australia

    Roberto Conti

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  1. Erik Bédos
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Correspondence to Erik Bédos.

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Communicated by Karlheinz Gröchenig.

E. Bédos was partially supported by the Norwegian Research Council.

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Bédos, E., Conti, R. On Twisted Fourier Analysis and Convergence of Fourier Series on Discrete Groups. J Fourier Anal Appl 15, 336–365 (2009). https://doi.org/10.1007/s00041-009-9067-z

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