2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67184Let $G$ be a reductive group in the Harish-Chandra class e.g. a connected semisimple Lie group with finite center, or the group of real points of a connected reductive algebraic group defined over $\R$. Let $σ$ be an involution of the Lie group $G$, $H$ an open subgroup of the subgroup of fixed points of $σ$. One decomposes the elements of $L^2(G/H)$ with the help of joint eigenfunctions under the algebra of left invariant differential operators under $G$ on $G/H$.Representation Theory22E46, 22F30, 22E30, 22E50, 33C67text