Analyse harmonique sur les groupes de Heisenberg généralisés
Let \(G=(X_ 1,X_ 2,X_ 3)_ B\) be the generalized Heisenberg group as defined by \textit{H. Reiter} in [Comment. Math. Helv. 49, 333-364 (1974; Zbl 0292.43007)]. Under some natural conditions on G involving not the separability, we clarify the unitary irreducible representations of G. We prove a Fourier inversion formula and determine a space of functions \(\phi\) on G for which \(\pi\) (\(\phi)\) is a Hilbert-Schmidt operator for every irreducible representation \(\pi\) of G.
scientific article; zbMATH DE number 3863502
scientific article