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Spanning L 2 of a nilpotent Lie group by eigenvectors of invariant differential operators

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Abstract

Let \(G=\exp (\frak g)\) be a non-abelian, connected, simply connected, nilpotent Lie group. We show that the eigenvectors of a finite number of families of left invariant differential operators and their conjugates span a dense subspace of L 2 (G). The restriction of the left regular representation to each one of these (left invariant) eigenspaces disintegrates into irreducible unitary representations with multiplicities 0 and 1 only.

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Authors and Affiliations

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

    J. Ludwig

  2. Unité de Recherche en Mathématiques, Université du Luxembourg, 162A, avenue de la Faïencerie, 1511, Luxembourg, Luxembourg

    C. Molitor-Braun

  3. 2, Rue des Fresnes, 57290, Fameck, France

    L. Scuto

Authors
  1. J. Ludwig
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  2. C. Molitor-Braun
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  3. L. Scuto
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Corresponding author

Correspondence to C. Molitor-Braun.

Additional information

J. Ludwig and C. Molitor-Braun are supported by the research grant R1F104C09 of the University of Luxembourg.

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Ludwig, J., Molitor-Braun, C. & Scuto, L. Spanning L 2 of a nilpotent Lie group by eigenvectors of invariant differential operators. Math. Z. 260, 717–753 (2008). https://doi.org/10.1007/s00209-007-0297-y

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  • DOI: https://doi.org/10.1007/s00209-007-0297-y

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