Izvestiya of Saratov University.
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

differential operators

About reversibility states of linear differential operators with periodic unbounded operator coefficients

For investigated linear differential operator (equation) with unbounded periodic operator coefficients defined at one of the Banach space of vector functions defined on all real axis difference operator (equation) with constant operator coefficient defined at appropriate Banach space of two-side vector sequences is considered. For differential and difference operators propositions about kernel and co-image dimensions coincidence, simultaneous complementarity of kernels and images, simultaneous reversibility, spectrum interrelation are proved.

On Inverse Periodic Problem for Differential Operators for Central Symmetric Potentials

An inverse spectral problem for Sturm–Liouville operators on a finite interval with periodic boundary conditions is studied in the central symmetric case, when the potential is symmetric with respect to the middle of the interval. We discuss the statement of the problem, provide an algorithm for its solution along with necessary and sufficient conditions for the solvability of this nonlinear inverse problem.

On Inverse Problem for Differential Operators with Deviating Argument

Second-order functional differential operators with a constant delay are considered. Properties of their spectral characteristics are obtained, and a nonlinear inverse spectral problem is studied, which consists in constructin goperators from the irspectra. We establish the unique nessand develop a constructive procedure for solution of the inverse problem.

On Recovering Differential Operators on a Closed Set from Spectra

The Sturm – Liouville differential operators on closed sets of the real line are considered. Properties of their spectral characteristics are obtained and the inverse problem of recovering the operators from their spectra is studied. An algorithm for the solution of the inverse problem is developed and the uniqueness of the solution is established. The statement and the study of inverse spectral problems essentially depend on the structure of the closed set.