Journal of Operator Theory

Volume 79, Issue 1, Winter 2018 pp. 213-223.

Ambarzumian theorem for non-selfadjoint boundary value problems

Authors: Olga Boyko (1), Olga Martynyuk (2), and Vyacheslav Pivovarchik (3)
Author institution: (1) Department of Applied Mathematics and Computer Science, South Ukrainian National Pedagogical University, Odesa, 65020, Ukraine
(2) Department of Higher Mathematics and Statistics, South Ukrainian National Pedagogical University, Odesa, 65020, Ukraine
(3) Department of Higher Mathematics and Statistics, South Ukrainian National Pedagogical University, Odesa, 65020, Ukraine

Summary: We prove analogues of Ambarzumian's theorem for the cases of: (1) the boundary value problem with dissipative conditions dependent on the spectral parameter at both ends, (2) the boundary value problem generated by the Sturm--Liouville equation with the potential linearly dependent of the spectral parameter.

DOI: http://dx.doi.org/10.7900/jot.2017feb14.2150
Keywords: Sturm-Liouville equation, von Neumann boundary conditions

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