A decomposition theorem for Jacobi forms
The author proves that the space of Jacobi forms of fixed degree, weight and index decomposes into a direct sum of the subspace of Jacobi cusp forms and subspaces consisting of Klingen-Eisenstein series derived from forms of smaller degree (Theorem 2). Such a decomposition theorem for Siegel modular forms is known due to \textit{H. Klingen} [Math. Z. 102, 30-43 (1967; Zbl 0155.40401)]. A characterization of Eisenstein series of different types by metrical properties using the Petersson scalar product for Jacobi forms is proved (Prop. 7). An application to the Fourier-Jacobi coefficients is given: one shows that in general there are more Jacobi forms than Fourier-Jacobi coefficients of Siegel modular forms (see Appendix).
scientific article; zbMATH DE number 840196