A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Groups with frames of translates

Volume 167 / 2022

Hartmut Führ, Vignon Oussa Colloquium Mathematicum 167 (2022), 73-91 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

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image