Proves that a discrete solution exists for the critical inverse eigenvalue problem by direct application of Gohberg's theorem.

http://iopscience.iop.org/article/10.1088/0305-4470/13/12/001/pdf

On the existence of a solution for a slab critical problem

Defines a general class of problem that has been termed the inverse eigenvalue problem. Basically similar problems have already been studied as isolated and specific examples in the analysis of time eigenvalues appearing in neutron transport theory. In this work, however, the authors present a general unified method for their treatment using functional analytic methods. Specifically, the critical slab problem has been analysed as an example of such an inverse eigenvalue problem of a Fredholm integral equation using the theory of perturbation of a class of positive, analytic operator-valued functions in Banach space. Numerical calculations of the critical thickness are given. These results are encouraging, considering the simplicity of the method, which does not involve an explicit solution of the Fredholm equation.

K Ganguly

Papers

Inverse eigenvalue problem for a finite multiplying slab