  The aim of this study is to investigate a class of generalized boundary value
transmission problems (BVTP's) for Sturm-Liouville equation on two separate
intervals. We introduce modified inner product in direct sum space
$L_{2}[a,c)\oplus L_{2}(c,b]\oplus\mathbb{C}^{2}$ and define symmetric linear
operator in it such a way that the considered problem can be interpreted as an
eigenvalue problem of this operator. Then by suggesting an own approaches we
construct Green's function for problem under consideration and find the
resolvent function for corresponding inhomogeneous problem.
