Аннотация:The spectrum of $L^2$ on a pseudo-unitary group $U(p,q)$ (we assume $p≥q$ naturally splits into $q+1$ types. We write explicitly orthogonal projectors in $L^2$ to subspaces with uniform spectra (this is an old question formulated by Gelfand and Gindikin). We also write two finer separations of $L^2$. In the first case pieces are enumerated by $r=0, 1,..., q$ and representations of discrete series of $U(p−r,q−r)$, where $r=0, \dots, q$. In the second case pieces are enumerated by all discrete parameters of the tempered spectrum of $U(p,q)$.
https://arxiv.org/abs/1703.08814