Green's Function of the Unspecified Space for the Helmholtz Equation with Variable Wave-Numbers

Let us consider two unbounded media having wave-numbers differing in a domain ω. Defining a function basis on ω, the authors construct a convergent series which represents the Green's function for the first medium in terms of that of the second medium; no “a priori” assumption is necessary. Two examples show that by a suitable choice of the first basis function the first term of the series provides a good approximation within the frequency range (0, ∞).