Fourier Multiplier Norms of Spherical Functions on the Generalized Lorentz Groups - Mathematics > Representation TheoryReport as inadecuate




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Abstract: Our main result provides a closed expression for the completely boundedFourier multiplier norm of the spherical functions on the generalized Lorentzgroups. As a corollary, we find that there is no uniform bound on thecompletely bounded Fourier multiplier norm of the spherical functions on thegeneralized Lorentz groups. We extend the latter result to the remainingconnected, real rank one, simple Lie groups with finite center, and as anapplication we obtain that each of the above mentioned groups has a completelybounded Fourier multiplier, which is not the coefficient of a uniformly boundedrepresentation of the group on a Hilbert space.



Author: Troels Steenstrup

Source: https://arxiv.org/



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