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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
.
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