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Inverse problem for Sturm-Liouville operators with a transmission and parameter dependent boundary conditions

Journal: Caspian Journal of Mathematical Sciences (Vol.6, No. 2)

Publication Date:

Authors : ; ;

Page : 107-119

Keywords : Inverse Sturm--Liouville equation; Non self-adjoint operator; Jump condition; Hilbert space;

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Abstract

In this manuscript, we consider the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. We prove by defining a new Hilbert space and using spectral data of a kind, the potential function can be uniquely determined by a set of value of eigenfunctions at an interior point and part of two sets of eigenvalues.

Last modified: 2018-01-18 00:58:42