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Winter 2018 Fourier multiplier norms of spherical functions on the generalized Lorentz groups
Troels Steenstrup
Adv. Oper. Theory 3(1): 193-230 (Winter 2018). DOI: 10.22034/aot.1706-1172

Abstract

Our main result provides a closed expression for the completely bounded Fourier multiplier norm of the spherical functions on the generalized Lorentz groups $SO_0(1,n)$ (for $n \geq 2$). 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 $n \geq 2$) and the exceptional group $F_{4(-20)}$, 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.

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Troels Steenstrup. "Fourier multiplier norms of spherical functions on the generalized Lorentz groups." Adv. Oper. Theory 3 (1) 193 - 230, Winter 2018. https://doi.org/10.22034/aot.1706-1172

Information

Received: 5 June 2017; Accepted: 19 June 2017; Published: Winter 2018
First available in Project Euclid: 5 December 2017

zbMATH: 1379.43009
MathSciNet: MR3730346
Digital Object Identifier: 10.22034/aot.1706-1172

Subjects:
Primary: 22E46
Secondary: 43A90, 46L07

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.3 • No. 1 • Winter 2018
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