Jacobi-like forms,differential equations,and Hecke operators

We construct a map from the space of Jacobi-like forms image omitted]() for a discrete subgroup image omitted] to the space image omitted] of sequences of meromorphic functions satisfying certain conditions determined by some linear ordinary differential operators and prove that the Hecke operator actions on image omitted]() and on image omitted] are compatible with respect to this map.