We give an elementary proof of a solvability criterion for the {\em boundary
Carath\'{e}odory-Fej\'{e}r problem}: given a point x∈R and, a finite set
of target values, to construct a function f in the Pick class such that the
first few derivatives of f take on the prescribed target values at x. We
also derive a linear fractional parametrization of the set of solutions of the
interpolation problem. The proofs are based on a reduction method due to Julia
and Nevanlinna.Comment: 30 pages. We have slightly improved the presentatio