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In this paper we are concerned with an inverse problem with Robin boundary conditions, which states that, when the potential on [ 0 , 1 / 2 ] and the coefficient at the left end point are known a priori, a full spectrum uniquely determines its potential on the whole interval and the coefficient at the right end point. We shall give a new method for reconstructing the potential for this problem in terms of the Mittag-Leffler decomposition of entire functions associated with this problem. The new reconstructing method also deduces a necessary and sufficient condition for the existence issue. [ABSTRACT FROM AUTHOR]

We consider the non-self-adjoint Sturm–Liouville operator on a finite interval. The inverse spectral problem is studied, which consists in recovering this operator from its eigenvalues and generalized weight numbers. We prove local solvability and stability of this inverse problem, relying on the method of spectral mappings. Possible splitting of multiple eigenvalues is taken into account. [ABSTRACT FROM AUTHOR]

In this paper, we consider a discontinuous Dirac operator with eigenparameter dependent both boundary and two transmission conditions. We introduce a suitable Hilbert space formulation and get some properties of eigenvalues and eigenfunctions. Then we investigate the Green's function, the resolvent operator, and some uniqueness theorems by using the Weyl function and some spectral data. [ABSTRACT FROM AUTHOR]