Journal of Fourier Analysis and Applications

, Volume 15, Issue 3, pp 336–365

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



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.


Twisted group C*-algebra Fourier series Fejér summation Abel-Poisson summation Amenable group Haagerup property Length function Polynomial growth Subexponential growth 

Mathematics Subject Classification (2000)

22D10 22D25 46L55 43A07 43A65 


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Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of OsloOsloNorway
  2. 2.Mathematics, School of Mathematical and Physical SciencesUniversity of NewcastleCallaghanAustralia
  3. 3.Department of MathematicsUniversity of Rome 2 Tor VergataRomeItaly

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