Sturm – Liouville operator

An Inverse Spectral Problem for Sturm – Liouville Operators with Singular Potentials on Graphs with a Cycle

Authors: Vasilev S. V.

This paper is devoted to the solution of inverse spectral problems for Sturm – Liouville operators with singular potentials from class W2−1 on graphs with a cycle. We consider the lengths of the edges of investigated graphs as commensurable quantities. For the spectral characteristics, we take the spectra of specific boundary value problems and special signs, how it is done in the case of classical Sturm – Liouville operators on graphs with a cycle. From the spectra, we recover the characteristic functions using Hadamard’s theorem.

On Inverse Problem for Sturm – Liouville Operator with Discontinuous Coefficients

Authors: Akhmedova E. N., Guseinov I. M.

In the paper uniqueness of reconstruction of the Sturm – Liouville operator with discontinuous coefficients by spectral data is proved and algorithm of construction of the potential is provided.