Related papers: Method for solving inverse spectral problems on qu…
We study an inverse spectral problem for arbitrary order ordinary differential equations on compact star-type graphs when differential equations have regular singularities at boundary vertices. As the main spectral characteristics we…
The inverse problem for the Sturm- Liouville operator with complex periodic potential and positive discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the…
This paper deals with the Sturm-Liouville problem that feature distribution potential, polynomial dependence on the spectral parameter in the first boundary condition, and analytical dependence, in the second one. We study an inverse…
A Neumann series of Bessel functions (NSBF) representation for solutions of Sturm-Liouville equations and for their derivatives is obtained. The representation possesses an attractive feature for applications: for all real values of the…
We suggest a new statement of the inverse spectral problem for Sturm--Liouville-type operators with constant delay. This inverse problem consists in recovering the coefficient (often referred to as potential) of the delayed term in the…
A spectral parameter power series (SPPS) representation for regular solutions of singular Bessel type Sturm-Liouville equations with complex coefficients is obtained as well as an SPPS representation for the (entire) characteristic function…
In this paper, we for the first time get constructive solution for the inverse Sturm-Liouville problem with complex-valued singular potential and with polynomials of the spectral parameter in the boundary conditions. The uniqueness of…
The inverse spectral problem is studied for the Sturm-Liouville operator with a complex-valued potential and arbitrary entire functions in one of the boundary conditions. We obtain necessary and sufficient conditions for uniqueness, and…
In this paper, inverse spectral problems for Sturm-Liouville operators on a tree (a graph without cycles) are studied. We show that if the potential on an edge is known a priori, then b - 1 spectral sets uniquely determine the potential…
We study inverse spectral problems for ordinary differential equations with regular singularities on compact star-type graphs when differential equations have different orders on diferent edges. As the main spectral characteristics we…
The inverse spectral problem is investigated for the matrix Sturm-Liouville equation on a finite interval. Properties of spectral characteristics are provided, a constructive procedure for the solution of the inverse problem along with…
Boundary value problems for Sturm-Liouville operators with potentials from the class $W_2^{-1}$ on a star-shaped graph are considered. We assume that the potentials are known on all the edges of the graph except two, and show that the…
In this paper, the Sturm-Liouville operators on a graph with a cycle are considered. We study the inverse spectral problem, which consists in the recovery of the potentials from several spectra and a sequence of signs related to the…
We suggest a new formulation of the inverse spectral problem for second-order functional-differential operators on star-shaped graphs with global delay. The latter means that the delay, being measured in the direction to a specific boundary…
Inverse problems of recovering the coefficients of Sturm-Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: (1) from the sequences of eigenvalues and norming constants; (2)…
In this study, the theorem on necessary and sufficient conditions for the solvability of inverse problem for Sturm-Liouville operator with discontinuous coefficient is proved and the algorithm of reconstruction of potential from spectral…
The inverse problem for the Sturm- Liouville operator with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator is…
We consider an inverse optimization spectral problem for the Sturm-Liouville operator $$\mathcal{L}[q] u:=-u''+q(x)u$$ subject to the separated boundary conditions. In the main result, we prove that this problem is related to the existence…
We consider the non-self-adjoint Sturm-Liouville operator on a finite interval. The inverse spectral problem is studied, which consists in recovering this operator from its eigenvalues and generalized weight numbers. We prove local…
We demonstrate how the inverse scattering problem of a quantum star graph can be solved by means of diagonalization of Hermitian unitary matrix when the vertex coupling is of the scale invariant (or F\"ul\H{o}p-Tsutsui) form. This enables…