Necessary and sufficient conditions for the solvability of the inverse problem for non-self-adjoint pencils of Sturm-Liouville operators on the half-line

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Published: Aug 24, 2011
DOI: https://doi.org/10.5556/j.tkjm.42.2011.742
Keywords:
Sturm-Liouville operators boundary conditions with the spectral parameter inverse spectral problems method of spectral mappings

Main Article Content

Vjacheslav Yurko
Department of Mathematics, Saratov University

Abstract

Non-self-adjoint Sturm-Liouville differential operators on the half-line with a boundary condition depending polynomially on the spectral parameter are studied. We investigate the inverse problem of recovering the operator from the Weyl function. For this inverse problem we provide necessary and suffcient conditions for its solvability along with a procedure for constructing its solution by the method of spectral mappings.

Article Details

How to Cite
Yurko, V. (2011). Necessary and sufficient conditions for the solvability of the inverse problem for non-self-adjoint pencils of Sturm-Liouville operators on the half-line. Tamkang Journal of Mathematics, 42(3), 247–258. https://doi.org/10.5556/j.tkjm.42.2011.742
Issue
Vol. 42 No. 3 (2011)
Section
Special Issue
Author Biography

Vjacheslav Yurko, Department of Mathematics, Saratov University

Department of Mathematics

Saratov University

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