AN INVERSE EIGENVALUE PROBLEM FOR AN ARBITRARY, MULTIPLY CONNECTED, BOUNDED DOMAIN IN R3 WITH IMPEDANCE BOUNDARY-CONDITIONS

The basic problem in this paper is that of determining the geometry of an arbitrary, multiply connected, bounded region in R3, together with the impedance boundary conditions, from a complete knowledge of the eigenvalues \{lambda(j)\}j=1 infinity, for the negative Laplacian -del-2 = -SIGMA(i=1)3 (partial derivative/partial derivative x(i))2 in the (x1, x2, x3)-space, using the asymptotic expansion of the spectral function THETA(t) = SIGMA(j=1) infinity exp (-t-lambda(j)) for small positive t.