Invariant transformations for the Sturm-Liouville operator

In this paper, we consider the Sturm-Liouville operator on a finite interval. For particular boundary conditions, a group of invariant transformations that preserve the operator spectrum is constructed. This result allows us to reconsider some old problems for the Sturm-Liouville operator. In particular, the influence of the group of transformations on the inverse problem is discussed. Bibliography: 13 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 327, 2005, pp. 25–54.