Let G be a compactly generated, locally compact group with polynomial growth and let ω be a weight on G. We look for general conditions on the weight which allow us to develop a functional calculus on a total part of L1(G,ω). This functional calculus is then used to study harmonic analysis properties of L1(G,ω), such as the Wiener property and Domar's theorem.
@article{urn:eudml:doc:44493,
title = {Functional calculus in weighted group algebras.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {17},
year = {2004},
pages = {321-357},
zbl = {1049.43001},
mrnumber = {MR2083958},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44493}
}
Dziubanski, Jacek; Ludwig, Jean; Molitor-Braun, Carine. Functional calculus in weighted group algebras.. Revista Matemática de la Universidad Complutense de Madrid, Tome 17 (2004) pp. 321-357. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44493/