  We re-analyse the bulk reconstruction for a scalar field in Lorentzian AdS
spacetime, both for the case of even and odd dimensions, for an extended range
of conformal dimensions where the original HKLL reconstruction has to be
modified. We also discuss the use of space-like Green's functions in the bulk
reconstruction. We demonstrate that in the extended range also the singular
part of the Green's function, omitted in the original papers, has be included.
The results are particularly simple and physically interesting for integer
conformal dimensions below the range considered in the original HKLL papers.
