Let K ⊂ ℝ3 be an open bounded strictly convex domain with smooth connected compact boundary ∂K. Set
We wish to study the filtered scattering amplitude, related to the transmission problem
Here w± are the limiting values of w on ∂Ω; from the Ω;± side, while ∂w±/∂n are the corresponding limiting values of the normal derivative ∂w?/∂n on ∂Ω;. The function α(x) ∈ C∞(K¯), called the index of refraction, has the property α(x) > 0 for x ∈ K¯.