Groups with frames of translates

Hartmut Führ, Vignon Oussa Colloquium Mathematicum MSC: Primary 22D10; Secondary 42C15. DOI: 10.4064/cm7864-10-2020 Published online: 22 April 2021

Abstract

Let $G$ be a locally compact group with left regular representation $\lambda _{G}$. We say that $G$ admits a frame of translates if there exist a countable set $\Gamma \subset G$ and $\varphi \in L^{2}(G)$ such that $(\lambda _{G}(x) \varphi )_{x \in \Gamma }$ is a frame for $L^{2}(G)$. The present work aims to characterize locally compact groups having frames of translates, and to this end, we derive necessary and/or sufficient conditions for the existence of such frames. Additionally, we exhibit surprisingly large classes of Lie groups admitting frames of translates.

Authors

  • Hartmut FührLehrstuhl A für Mathematik
    RWTH Aachen University
    D-52056 Aachen, Germany
    e-mail
  • Vignon OussaDepartment of Mathematics
    Bridgewater State University
    Bridgewater, MA 02324, U.S.A.
    e-mail

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