Weak convergence of spectral shift functions revisited
| Autor: | Connard, Carson, Ingimarson, Benjamin, Nichols, Roger, Paul, Andrew |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | We study convergence of the spectral shift function for the finite interval restrictions of a pair of full-line Schr\"odinger operators to an interval of the form $(-\ell,\ell)$ with coupled boundary conditions at the endpoints as $\ell\to \infty$ in the case when the finite interval restrictions are relatively prime to those with Dirichlet boundary conditions. Using a Krein-type resolvent identity we show that the spectral shift function for the finite interval restrictions converges weakly to that for the pair of full-line Schr\"odinger operators as the length of the interval tends to infinity. Comment: 23 pages |
| Databáze: | arXiv |
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