Nilpotent Lie Groups: Fourier Inversion and Prime Ideals View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-04

AUTHORS

Ying-Fen Lin, Jean Ludwig, Carine Molitor-Braun

ABSTRACT

We establish a Fourier inversion theorem for general connected, simply connected nilpotent Lie groups G=exp(g) by showing that operator fields defined on suitable sub-manifolds of g∗ are images of Schwartz functions under the Fourier transform. As an application of this result, we provide a complete characterisation of a large class of invariant prime closed two-sided ideals of L1(G) as kernels of sets of irreducible representations of G. More... »

PAGES

345-376

References to SciGraph publications

  • 1994-12. Matrix coefficients and a Weyl correspondence for nilpotent Lie groups in INVENTIONES MATHEMATICAE
  • 1983-03. On primary ideals in the group algebra of a nilpotent Lie group in MATHEMATISCHE ANNALEN
  • 1984-11. Über das Synthese-Problem für nilpotente Liesche Gruppen in MATHEMATISCHE ANNALEN
  • 1994-01. On the nilpotent * - Fourier transform in LETTERS IN MATHEMATICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00041-017-9586-y

    DOI

    http://dx.doi.org/10.1007/s00041-017-9586-y

    DIMENSIONS

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