Fourier multiplier norms of spherical functions on the generalized Lorentz groups

Troels Steenstrup*

*Corresponding author for this work

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Abstract

Our main result provides a closed expression for the completely bounded Fourier multiplier norm of the spherical functions on the generalized Lorentz groups SO0(1, n) (for n ≥ 2). As a corollary, we find that there is no uniform bound on the completely bounded Fourier multiplier norm of the spherical functions on the generalized Lorentz groups. We extend the latter result to the groups SU(1, n), Sp(1, n) (for n ≥ 2) and the exceptional group F4(-20), and as an application we obtain that each of the above mentioned groups has a completely bounded Fourier multiplier, which is not the coefficient of a uniformly bounded representation of the group on a Hilbert space.

Original languageEnglish
JournalAdvances in Operator Theory
Volume3
Issue number1
Pages (from-to)193-230
DOIs
Publication statusPublished - 2018

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Keywords

  • Completely bounded Fourier multiplier norm
  • Generalized Lorentz group
  • Lie group
  • Representation
  • Spherical function

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