Factorisation of Non-negative Fredholm Operators and Inverse Spectral Problems for Bessel Operators

Abstract

We study the problem of factorisation of non-negative Fredholm operators acting in the Hilbert space L2(0, 1) and its relation to the inverse spectral problem for Bessel operators. In particular, we derive an algorithm of reconstructing the singular potential of the Bessel operator from its spectrum and the sequence of norming constants.