Geodesic
Weight functions on groups and an amenability criterion for Beurling algebras
Matematičeskie zametki, Tome 60 (1996) no. 3, pp. 370-382

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is devoted to the study of weights on groups. A connection between weight functions and harmonic functions is established. A relationship between the weight theory on groups with the “Tychonoff property” and the theory of bounded cohomology is presented. It is proved that the Beurling algebra $l^1(G,\omega)$ constructed for the weight $\omega$ is amenable if and only if the group $G$ is amenable and the weight $\omega$ is equivalent to a multiplicative character $\chi\colon G\to\mathbb R_+$. 
@article{MZM_1996_60_3_a4,
     author = {R. I. Grigorchuk},
     title = {Weight functions on groups and an amenability criterion for {Beurling} algebras},
     journal = {Matemati\v{c}eskie zametki},
     pages = {370--382},
     publisher = {mathdoc},
     volume = {60},
     number = {3},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_60_3_a4/}
}
TY  - JOUR
AU  - R. I. Grigorchuk
TI  - Weight functions on groups and an amenability criterion for Beurling algebras
JO  - Matematičeskie zametki
PY  - 1996
SP  - 370
EP  - 382
VL  - 60
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1996_60_3_a4/
LA  - ru
ID  - MZM_1996_60_3_a4
ER  - 
%0 Journal Article
%A R. I. Grigorchuk
%T Weight functions on groups and an amenability criterion for Beurling algebras
%J Matematičeskie zametki
%D 1996
%P 370-382
%V 60
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1996_60_3_a4/
%G ru
%F MZM_1996_60_3_a4
R. I. Grigorchuk. Weight functions on groups and an amenability criterion for Beurling algebras. Matematičeskie zametki, Tome 60 (1996) no. 3, pp. 370-382. http://geodesic.mathdoc.fr/item/MZM_1996_60_3_a4/