  In this paper we will show several properties of the Green's functions
related to various boundary value problems of arbitrary even order. In
particular, we will write the expression of the Green's functions related to
the general differential operator of order 2n coupled to Neumann, Dirichlet and
mixed boundary conditions, as a linear combination of the Green's functions
corresponding to periodic conditions on a different interval.
  This will allow us to ensure the constant sign of various Green's functions
and to deduce spectral results.
