El-Raheem, Z. (2015). The inverse spectral problem of some singular version of one-dimensional Schro¨dinger operator with explosive factor in finite interval. test, 23(2), 271-277. doi: 10.1016/j.joems.2014.05.007
Zaki F.A. El-Raheem. "The inverse spectral problem of some singular version of one-dimensional Schro¨dinger operator with explosive factor in finite interval". test, 23, 2, 2015, 271-277. doi: 10.1016/j.joems.2014.05.007
El-Raheem, Z. (2015). 'The inverse spectral problem of some singular version of one-dimensional Schro¨dinger operator with explosive factor in finite interval', test, 23(2), pp. 271-277. doi: 10.1016/j.joems.2014.05.007
El-Raheem, Z. The inverse spectral problem of some singular version of one-dimensional Schro¨dinger operator with explosive factor in finite interval. test, 2015; 23(2): 271-277. doi: 10.1016/j.joems.2014.05.007

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, Pages 271-277    PDF (491.35 K)
Document Type: Original Article
DOI: 10.1016/j.joems.2014.05.007
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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