Local solvability and stability of inverse problems for Sturm-Liouville operators with a discontinuity

Chuan-Fu Yang; Natalia P. Bondarenko

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arXiv · 1906.06552

Local solvability and stability of inverse problems for Sturm-Liouville operators with a discontinuity

Chuan-Fu Yang·Natalia P. Bondarenko

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Abstract

Partial inverse problems are studied for Sturm-Liouville operators with a discontinuity. The main results of the paper are local solvability and stability of the considered inverse problems. Our approach is based on a constructive algorithm for solving the inverse problems. The key role in our method is played by the Riesz-basis property of a special vector-functional system in a Hilbert space. In addition, we obtain a new uniqueness theorem for recovering the potential on a part of the interval, by using a fractional part of the spectrum.

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BibTeX RIS

Chuan-Fu Yang, Natalia P. Bondarenko. 2019-06-15. Local solvability and stability of inverse problems for Sturm-Liouville operators with a discontinuity. https://arxiv.org/abs/1906.06552

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