Generalized Poincaré series for \(\operatorname{SU}(2,1)\) (Q6631397)

In the paper under the review, the authors define and study Poincaré series attached to the Stone-von Neumann representation of the maximal unipotent subgroup of \(\mathrm{SU}(2,1)\). Using the Fourier term modules, the authors refine the results of \textit{R. Miatello} and \textit{N. R. Wallach} [J. Funct. Anal. 86, No. 2, 411--487 (1989; Zbl 0692.10029)] to compute the inner product of truncations of Poincaré series with square-integrable automorphic forms. As a main result, it is proven that all square-integrable automorphic forms occur in relation to Poincaré series.