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: 2017-07-01
Authors : Mohammad Shahriari; Ali Asghar Jodayree Akbarfam;
Page : 107-119
Keywords : Inverse Sturm--Liouville equation; Non self-adjoint operator; Jump condition; Hilbert space;
Abstract
n 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.
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