Domains of time-dependent density-potential mappings

The key element in time-dependent density functional theory is the one-to-one correspondence between the one-particle density and the external potential. In most approaches, this mapping is transformed into a certain type of Sturm-Liouville problem. Here we give conditions for existence and uniqueness of solutions and construct the weighted Sobolev space they lie in. As a result, the class of upsilon-representable densities is considerably widened with respect to previous work.