The asymptotic behavior of the Green function of the boundary-value problem for a second-order equation on a geometric graph

The boundary-value problem (where s is a complex parameter with Re s > 0) on an open connected geometric graph is considered. The asymptotic behavior as Im s → ∞ of the Green function is determined; it implies that the Green function has a preimage under the one-sided Laplace transform. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 38, Suzdal Conference-2004, Part 3, 2006.