Panakhov, Etibar S.; Bas, Erdal Inverse problem having special singularity type from two spectra. (English) Zbl 1300.34039 Tamsui Oxf. J. Inf. Math. Sci. 28, No. 3, 239-258 (2012). Summary: It is well-known that the two spectra \(\{\lambda_n\}\) and \(\{\mu_n\}\) uniquely determine the potential function \(q(x)\) in a Sturm-Liouville equation defined on the unit interval and having the special singularity \(q(x)={\delta\over x^p}+ q_0(x)\) (where \(\delta\) is an constant, \(1<p<2\)) at the point zero. In this work, we give the solution of the inverse problem on two partially non-coinciding spectra for the Sturm-Liouville equation with to peculiarity at zero. In particular, we obtain Hochstadt’s theorem concerning the structure of the difference \(q(x)-\widetilde g(x)\). Cited in 2 Documents MSC: 34A55 Inverse problems involving ordinary differential equations 34B24 Sturm-Liouville theory 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) Keywords:inverse problem; singular Sturm-Liouville operator; spectra; Hochstadt theorem PDFBibTeX XMLCite \textit{E. S. Panakhov} and \textit{E. Bas}, Tamsui Oxf. J. Inf. Math. Sci. 28, No. 3, 239--258 (2012; Zbl 1300.34039)