Abstract
Consider two inverse problems for Sturm–Liouville problems on the unit interval. This means that there are two corresponding mappings \(F, f\) from a Hilbert space of potentials \(H\) into their spectral data. They are called isomorphic if \(F\) is a composition of \(f\) and some isomorphism \(U\) of \(H\) onto itself. An isomorphic class is a collection of inverse problems isomorphic to each other. We consider basic Sturm–Liouville problems on the unit interval and on the circle and describe their isomorphic classes of inverse problems. For example, we prove that the inverse problems for the case of Dirichlet and Neumann boundary conditions are isomorphic. The proof is based on nonlinear analysis.
DOI 10.1134/S1061920824601745
