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

Article

DOI: 10.1007/s00041-009-9067-z

Cite this article as:
Bédos, E. & Conti, R. J Fourier Anal Appl (2009) 15: 336. doi:10.1007/s00041-009-9067-z

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.

Keywords

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 

Copyright information

© Birkhäuser Boston 2009

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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