A+ CATEGORY SCIENTIFIC UNIT

Spectral synthesis in $L^2(G)$

Volume 138 / 2015

Jean Ludwig, Carine Molitor-Braun, Sanjoy Pusti Colloquium Mathematicum 138 (2015), 89-103 MSC: Primary 43A45, 43A85; Secondary 22E30. DOI: 10.4064/cm138-1-6

Abstract

For locally compact, second countable, type I groups $G$, we characterize all closed (two-sided) translation invariant subspaces of $L^2(G)$. We establish a similar result for $K$-biinvariant $L^2$-functions ($K$ a fixed maximal compact subgroup) in the context of semisimple Lie groups.

Authors

  • Jean LudwigUniversité de Lorraine
    Institut Élie Cartan de Lorraine
    UMR 7502
    F-57045 Metz, France
    e-mail
  • Carine Molitor-BraunMathematics Research Unit
    University of Luxembourg
    Campus Kirchberg
    6, rue Richard Coudenhove-Kalergi
    L-1359, Luxembourg
    e-mail
  • Sanjoy PustiMathematics Research Unit
    University of Luxembourg
    Campus Kirchberg
    6, rue Richard Coudenhove-Kalergi
    L-1359, Luxembourg
    and
    Department of Mathematics and Statistics
    Indian Institute of Technology
    Kanpur, India 208016
    e-mail

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