An Inverse Problem for Sturm–Liouville Operators with a Piecewise Entire Potential and Discontinuity Conditions of Solutions on a Curve

• Published in: Siberian mathematical journal Vol. 64; no. 3; pp. 542 - 553
• Main Author: Golubkov, A. A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-05-2023; Springer Nature B.V
• Subjects: Discontinuity; Inverse problems; Liouville equations; Mathematics; Mathematics and Statistics; Transfer matrices; inverse problem; discontinuity conditions of a solution; 517.984
• ISSN: 0037-4466; 1573-9260
• DOI: 10.1134/S0037446623030047

Under consideration is a Sturm–Liouville equation with a piecewise entire potential and discontinuity conditions independent of the spectral parameter for the solutions on an unspecified rectifiable curve lying in the complex plane. We study an inverse spectral problem with respect to the ratio of elements of one column or one row of the transfer matrix and give the conditions of uniqueness of a solution. These results are applied to the inverse problem for the Sturm–Liouville equation with piecewise constant complex weight, piecewise entire potential, and discontinuity conditions on a segment.