Abstract
We give a short review of results on inverse spectral problems for second-order differential operators on an interval with non-separated boundary conditions. We pay the main attention to the most important nonlinear inverse problems of recovering coefficients of differential operators from given spectral characteristics. In the first part of the review, we provide the main results and methods related to inverse problems for Sturm–Liouville operators with non-separated boundary conditions: periodic, quasi-periodic and Robin-type boundary conditions. At the end, we present the main results on inverse problems for differential pencils with non-separated boundary conditions.
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 19-01-00102
Funding statement: This work was supported in part by Grant 1.1660.2017/4.6 of the Russian Ministry of Education and Science and by Grant 19-01-00102 of Russian Foundation for Basic Research.
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Uniqueness for the inverse fixed angle scattering problem
- Solving a backward problem for a distributed-order time fractional diffusion equation by a new adjoint technique
- A logarithmic estimate for the inverse source scattering problem with attenuation in a two-layered medium
- A non-iterative method for recovering the space-dependent source and the initial value simultaneously in a parabolic equation
- FEM-based Scalp-to-Cortex EEG data mapping via the solution of the Cauchy problem
- Multi-frame super resolution via deep plug-and-play CNN regularization
- On the Hochstadt–Lieberman type problem with eigenparameter dependent boundary condition
- Inverse spectral problems for differential operators with non-separated boundary conditions
Artikel in diesem Heft
- Frontmatter
- Uniqueness for the inverse fixed angle scattering problem
- Solving a backward problem for a distributed-order time fractional diffusion equation by a new adjoint technique
- A logarithmic estimate for the inverse source scattering problem with attenuation in a two-layered medium
- A non-iterative method for recovering the space-dependent source and the initial value simultaneously in a parabolic equation
- FEM-based Scalp-to-Cortex EEG data mapping via the solution of the Cauchy problem
- Multi-frame super resolution via deep plug-and-play CNN regularization
- On the Hochstadt–Lieberman type problem with eigenparameter dependent boundary condition
- Inverse spectral problems for differential operators with non-separated boundary conditions