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The aim of this paper is to show certain properties of the Green's functionsrelated to the Hill's equation coupled with different two point boundary valueconditions. We will obtain the expression of the Green's function of Neumann,Dirichlet, Mixed and anti-periodic problems as a combination of the Green'sfunction related to periodic ones.  As a consequence we will prove suitable results in spectral theory and deducesome comparison results for the solutions of the Hill's equation with differentboundary value conditions.

Green's Functions and Spectral Theory for the Hill's Equation