The inverse spectral problem of some singular version of one-dimensional Schro¨dinger operator with explosive factor in finite interval | ||||
| Journal of the Egyptian Mathematical Society | ||||
| Volume 23, Issue 2, 2015, Page 271-277 PDF (491.35 K) | ||||
| Document Type: Original Article | ||||
| DOI: 10.1016/j.joems.2014.05.007 | ||||
 View on SCiNiTO | ||||
| Author | ||||
| Zaki F.A. El-Raheem* | ||||
| Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt | ||||
| Abstract | ||||
| The inverse spectral problem is investigated for some singular version of one-dimensional Schro¨dinger operator with explosive factor on finite interval ½0; p. In the present paper the explosive factor subdivides the problem into two parts, with different characteristic, which causes a lot of analytical difficulties. We define the spectral data of the problem, derive the main integral equation and show that the potential is uniquely recovered for both parts of the problem. | ||||
| Keywords | ||||
| Dirichlet problem; Inverse problem; Contour integration; Spectral data; Main integral equation (Gelfand–Levitan integral equation); Uniqueness theorem | ||||
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