2019/01/01 by Jun Yan, Yan, Jun, Guoliang Shi +1
Mathematics · #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1901.00119
openalex publication_date 2019/01/01 · openalex created_date 2019/01/11 · openalex updated_date 2026/07/28
This paper deals with the inverse spectral problem for a non-self-adjoint Sturm-Liouville operator with discontinuous conditions inside the interval. We obtain that if the potential q is known a priori on a subinterval [ b,π] with b∈ ( d,π] or b=d, then h, β, γ and q on [ 0,π] can be uniquely determined by partial spectral data consisting of a sequence of eigenvalues and a subsequence of the corresponding generalized normalizing constants or a subsequence of the pairs of eigenvalues and the corresponding generalized ratios. For the case b∈ ( 0,d) , a similar statement holds if β, γ are also known a priori. Moreover, if q satisfies a local smoothness condition, we provide an alternative approach instead of using the high-energy asymptotic expansion of the Weyl m-function to solve the problem of missing eigenvalues and norming constants.