Xu, Xiao-Chuan On the direct and inverse transmission eigenvalue problems for the Schrödinger operator on the half line. (English) Zbl 1459.34068 Math. Methods Appl. Sci. 43, No. 15, 8434-8448 (2020). The following transmission boundary value problem is considered: \[ -\psi''+q(x)\psi=\lambda \psi,\; -\psi_0''=\lambda\psi_0,\; 0<x<1, \] \[ \psi'(0)-h\psi(0)=\psi'_0(0)-h\psi_0(0)=0,\; \psi_0(1)=\psi(1),\; \psi_0'(1)=\psi'(1). \] The eigenvalue asymptotics is established, and the inverse problem of recovering \(q\) from the spectrum is studied. Under additional assumptions the uniqueness theorem is proved for this inverse problem. Reviewer: Vjacheslav Yurko (Saratov) Cited in 3 Documents MSC: 34A55 Inverse problems involving ordinary differential equations 34L25 Scattering theory, inverse scattering involving ordinary differential operators 34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) Keywords:Sturm-Liouville equations; transmission boundary value problem; eigenvalue asymptotics; inverse spectral problem PDFBibTeX XMLCite \textit{X.-C. Xu}, Math. Methods Appl. Sci. 43, No. 15, 8434--8448 (2020; Zbl 1459.34068) Full Text: DOI arXiv