Abstract
The spectral function , where are the eigenvalues of the negative Laplacian in the (x1, x2, x3)-space, is studied for a general doubly-connected bounded region Ω in R3 with a smooth inner bounding surface S1 and a smooth outer bounding surface S2, where a finite number of piecewise smooth impedance boundary conditions on the parts S∗ 1, …, S∗ k of S1 and S∗ k+1, …, S∗ m of S2 are considered, such that and .