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Weighted group algebras on groups of polynomial growth

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Abstract.

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 L 1(G,ω). In particular, if the weight ω is sub-exponential, then the algebra L 1(G,ω) is symmetric. For these weights we develop a functional calculus on a total part of L 1(G,ω) and use it to prove the Wiener property.

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Authors and Affiliations

  1. Finstertal 16, 69514, Laudenbach, Germany

    G. Fendler

  2. Department of Mathematics, The University of Connecticut, Storrs, CT, 06269-3009, USA

    K. Gröchenig

  3. Institut für Angewandte Mathematik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 294, 69120, Heidelberg, Germany

    M. Leinert

  4. Département de Mathématiques, Université de Metz, Ile de Saulcy, 57045, Metz cedex 1, France

    J. Ludwig

  5. Séminaire de mathématique, Centre Universitaire de Luxembourg, 162A, Avenue de la Faï encerie, 1511, Luxembourg, Luxembourg

    C. Molitor-Braun

Authors
  1. G. Fendler
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  2. K. Gröchenig
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  3. M. Leinert
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  4. J. Ludwig
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  5. C. Molitor-Braun
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Corresponding author

Correspondence to K. Gröchenig.

Additional information

Mathematics Subject Classification (2000):43A20, 22D15, 22D12.

Supported by the Austrian Science Foundation project FWF P-14485.

Supported by the research grants MEN/CUL/98/007 and CUL/01/014.

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Fendler, G., Gröchenig, K., Leinert, M. et al. Weighted group algebras on groups of polynomial growth. Math. Z. 245, 791–821 (2003). https://doi.org/10.1007/s00209-003-0571-6

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  • DOI: https://doi.org/10.1007/s00209-003-0571-6

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