Inverse spectral problem for the one-dimensional Stark operator on the half-axis
UDC 517.91 We consider the Stark operator $T=-\dfrac{d^{2}}{dx^{2}}+x+q\left(x\right)$ on the half-axis $0\le x<\infty $ with a Dirichlet boundary condition at zero. By using transformation operators, we study the direct and inverse spectral problems and obtain the main integral equation...
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| Date: | 2020 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2020
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2302 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.91
We consider the Stark operator $T=-\dfrac{d^{2}}{dx^{2}}+x+q\left(x\right)$ on the half-axis $0\le x<\infty $ with a Dirichlet boundary condition at zero. By using transformation operators, we study the direct and inverse spectral problems and obtain the main integral equation for the inverse problem. We prove that the main integral equation is uniquely solvable and suggest an effective algorithm of reconstruction for the perturbed potential. |
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| DOI: | 10.37863/umzh.v72i4.2302 |