On twisted Fourier analysis and convergence of Fourier series on discrete groups
Bedos, Erik ; Conti, Roberto
arXiv, 0605145 / Harvested from arXiv
Text on arXiv
We study norm convergence and summability of Fourier series in the setting of reduced twisted group $C^*$-algebras of discrete groups. For amenable groups, F{\o}lner nets give the key to Fej\'er 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.
Publié le : 2006-05-05
Classification:  Mathematics - Operator Algebras,  Mathematical Physics,  Mathematics - Functional Analysis,  Mathematics - Group Theory,  22D10,  22D25,  46L55,  43A07,  43A65 
@article{0605145,
     author = {Bedos, Erik and Conti, Roberto},
     title = {On twisted Fourier analysis and convergence of Fourier series on
  discrete groups},
     journal = {arXiv},
     volume = {2006},
     number = {0},
     year = {2006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0605145}
}

Bedos, Erik; Conti, Roberto. On twisted Fourier analysis and convergence of Fourier series on
  discrete groups. arXiv, Tome 2006 (2006) no. 0, . http://gdmltest.u-ga.fr/item/0605145/