  Kohnen introduced a limit process for Siegel modular forms that produces
Jacobi forms. He asked if there is a space of real-analytic Siegel modular
forms such that skew-holomorphic Jacobi forms arise via this limit process. In
this paper, we initiate the study of harmonic skew-Maass-Jacobi forms and
harmonic Siegel-Maass forms. We improve a result of Maass on the Fourier
coefficients of harmonic Siegel-Maass forms, which allows us to establish a
connection to harmonic skew-Maass-Jacobi forms. In particular, we answer
Kohnen's question in the affirmative.
