Weighted group algebras on groups of polynomial growth
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- Fendler, G., Gröchenig, K., Leinert, M. et al. Math. Z. (2003) 245: 791. doi:10.1007/s00209-003-0571-6
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Let G be a compactly generated group of polynomial growth and ω a weight function on G. For a large class of weights we characterize symmetry of the weighted group algebra L1(G,ω). In particular, if the weight ω is sub-exponential, then the algebra L1(G,ω) is symmetric. For these weights we develop a functional calculus on a total part of L1(G,ω) and use it to prove the Wiener property.