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

2019/06/15 by Chuan‐Fu Yang, Yang, Chuan-Fu, Natalia P. Bondarenko +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1906.06552

openalex publication_date 2019/06/15 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

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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