The eigenvalues’ function (EVF) of the family of Sturm-Liouville operators and the inverse problems

We prove that the union of the spectra of the family of operators of Sturm-Liouville operators (generated by potential q and the family of separated boundary conditions) can be presented as a smooth surface, which we call EVF. We give the algorithm of reconstruction of q by EVF and prove that some uniqueness theorems in inverse problems follow from the properties of EVF. We apply EVF to problem of translation eigenvalues.