Abstract
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.
Highlights
1 Introduction The paper concerns the theory of inverse spectral problems for differential operators
The aim of this paper is to investigate local solvability and stability of Inverse problem 1.1 in the non-self-adjoint case
In [15], some results on local solvability and stability were obtained for the inverse problem of recovering the non-self-adjoint Sturm–Liouville operator with the Dirichlet boundary conditions from generalized spectral data (GSD)
Summary
The paper concerns the theory of inverse spectral problems for differential operators. The aim of this paper is to investigate local solvability and stability of Inverse problem 1.1 in the non-self-adjoint case. Buterin and Kuznetsova [20] proved local solvability and stability for the inverse problem by two spectra for the nonself-adjoint Sturm–Liouville operator They took splitting of multiple eigenvalues into account. In [15], some results on local solvability and stability were obtained for the inverse problem of recovering the non-self-adjoint Sturm–Liouville operator with the Dirichlet boundary conditions from GSD. In our sequel studies [21, 22], the results of this paper are applied to investigate the non-self-adjoint Sturm–Liouville problem with arbitrary entire functions in the boundary condition. Theorems 2.2 and 2.3 generalize their analogue for the self-adjoint case [8, Theorem 1.6.4]
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