Inverse Eigenvalue Problems for Singular Rank One Perturbations of a Sturm-Liouville Operator

This paper is concerned with the inverse eigenvalue problem for singular rank one perturbations of a Sturm-Liouville operator. We determine uniquely the potential function from the spectra of the Sturm-Liouville operator and its rank one perturbations.

Identification of the Domain of the Sturm–Liouville Operator on a Star Graph

This article is devoted to the unique recovering of the domain of the Sturm–Liouville operator on a star graph. The domain of the Sturm–Liouville operator is uniquely identified from the set of spectra of a finite number of specially selected canonical problems. In the general case, the domain of the definition of the original operator can be specified by integro-differential linear forms. In the case when the domain of the Sturm–Liouville operator on a star graph corresponds to the boundary value problem, it is sufficient to choose only finite parts of the spectra of canonical problems for a unique identification of the boundary form. Moreover, the above statement is valid only for a symmetric star graph.

About the Storm-Liouville operator with negative parameter in space L2(R)

In this paper, the question of the existence of a resolvent is studied, and also, after closure in space, the smoothness of functions from the domain of an operator of the unbounded type in an unbounded domain with coefficients strongly increasing at infinity is investigated.