On a specific heat-phonon spectrum inversion problem. Exact solution, unique existence theorem and Riemann hypothesis

Abstract

In this paper a problem and an integral equation, determining the phonon density of states by a measured lattice specific heat, are suggested. Its exact solution formula, unique existence theorem, the technique for eliminating divergence and some exact soluble models are given. The possible relation between the unique existence theorem for the inversion problem in physics and the Riemann hypothesis, which is an unsolved problem in mathematics, is also discussed.