RMC - Vol. 17 Num. 2, Dziubanski et al.

Full paper in PDF:
$% J. Dziubanski, J. Ludwig, and C. Molitor-Braun, Functional calculus in weighted group algebras, Rev. Mat. Complut. 17 (2004), 321–357.%$

Functional Calculus in Weighted Group Algebras

Jacek DZIUBANSKI, Jean LUDWIG,
and Carine MOLITOR-BRAUN

Institute of Mathematics Wroclaw University Pl. Grunwaldzki 2/4 — Poland jdziuban@math.uni.wroc.pl	Département de Mathématiques Université de Metz Ile de Saulcy F-57045 Metz cedex 1 — France ludwig@poncelet.sciences.univ-metz.fr

Laboratoire de Mathématiques
Université du Luxembourg
162A, Avenue de la Faïencerie
L-1511 Luxembourg — Luxembourg

carine.molitor@uni.lu

Received: April 9, 2003
Accepted: January 12, 2004

ABSTRACT

Let $G$ be a compactly generated, locally compact group with polynomial growth and let $w$ 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 $1 L (G,w)$ . This functional calculus is then used to study harmonic analysis properties of $1 L (G,w)$ , such as the Wiener property and Domar’s theorem.

Key words: weight, weighted group algebra, functional calculus, Wiener property
2000 Mathematics Subject Classification: 43A20.