  We consider a general one-particle Hamiltonian H = - \Delta_r + u(r) defined
in a d-dimensional domain. The object of interest is the time-independent Green
function G_z(r,r') = < r | (z-H)^{-1} | r' >. Recently, in one dimension (1D),
the Green's function problem was solved explicitly in inverse form, with
diagonal elements of Green's function as prescribed variables. The first aim of
this paper is to extract from the 1D inverse solution such information about
Green's function which cannot be deduced directly from its definition. Among
others, this information involves universal, i.e. u(r)-independent, behavior of
Green's function close to the domain boundary. The second aim is to extend the
inverse formalism to higher dimensions, especially to 3D, and to derive the
universal form of Green's function for various shapes of the confining domain
boundary.
