Inverse scattering on the line for Schr\'odinger operators with Miura potentials, II. Different Riccati representatives
| Autor: | Hryniv, R. O., Mykytyuk, Ya. V., Perry, P. A. |
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| Rok vydání: | 2009 |
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| Druh dokumentu: | Working Paper |
| Popis: | This is the second in a series of papers on scattering theory for one-dimensional Schr\"odinger operators with Miura potentials admitting a Riccati representation of the form $q=u'+u^2$ for some $u\in L^2(R)$. We consider potentials for which there exist `left' and `right' Riccati representatives with prescribed integrability on half-lines. This class includes all Faddeev--Marchenko potentials in $L^1(R,(1+|x|)dx)$ generating positive Schr\"odinger operators as well as many distributional potentials with Dirac delta-functions and Coulomb-like singularities. We completely describe the corresponding set of reflection coefficients $r$ and justify the algorithm reconstructing $q$ from $r$. Comment: 32 pages |
| Databáze: | arXiv |
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