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In three-dimensional case, we consider two classical operators: Schrodingeroperator and an operator in the divergence form. For slowly-decayingoscillating potentials, we establish spatial asymptotics of the Green'sfunction. The main term in this asymptotics involves vector-valued analyticfunction whose behavior is studied away from the spectrum. The absolutecontinuity of the spectrum is established as a corollary. For the operator inthe divergence form, we consider the wave equation and establish existence ofwave operators.

Spatial asymptotics of Green's function for elliptic operators and applications: a.c. spectral type, wave operators for wave equations