Eigenforms of the Laplacian on real and complex hyperbolic spaces (Q1103931)

A full space H p of solutions of the equation \(\Delta \alpha =c\alpha\) is described; here \(\Delta\) is the Laplacian, \(\alpha\) is a p-form on the real or complex hyperbolic n-space X and c is a complex constant. It is proved that for \(c\neq 0\) H p is isomorphic to the space \(C^{- \omega}(\oplus E_ i)\) of hyperfunction sections of \(\oplus E_ i\), \(E_ i\) are irreducible homogeneous vector bundles over \(\partial X\) and intertwining operator is called to be a Poisson transform. For \(c=0\) and \(0<p<\dim_{{\mathbb{R}}}X\) these spaces are non-isomorphic and a ``measure'' of this non-isomorphicness is investigated.