@article{Knudby_2017, title={Fourier algebras of parabolic subgroups}, volume={120}, url={https://www.mscand.dk/article/view/25624}, DOI={10.7146/math.scand.a-25624}, abstractNote={<p>We study the following question: given a locally compact group when does its Fourier algebra coincide with the subalgebra of the Fourier-Stieltjes algebra consisting of functions vanishing at infinity? We provide sufficient conditions for this to be the case.</p><p>As an application, we show that when $P$ is the minimal parabolic subgroup in one of the classical simple Lie groups of real rank one or the exceptional such group, then the Fourier algebra of $P$ coincides with the subalgebra of the Fourier-Stieltjes algebra of $P$ consisting of functions vanishing at infinity. In particular, the regular representation of $P$ decomposes as a direct sum of irreducible representations although $P$ is not compact.</p>}, number={2}, journal={MATHEMATICA SCANDINAVICA}, author={Knudby, Søren}, year={2017}, month={May}, pages={272–290} }