The purpose of this paper is to investigate the Cauchy problem for the Gross-Pitaevskii infinite linear hierarchy of equations on R(n), n >= 1. We prove local existence and uniqueness of solutions in certain Sobolev-type spaces H(xi)(alpha) of sequences of marginal density operators with alpha > n/2. In particular, we give a clear discussion of all cases alpha > n/2, which covers the local well-posedness problem for the Gross-Pitaevskii hierarchy in this situation. (C)...
